共查询到20条相似文献,搜索用时 156 毫秒
1.
David S. Metzler 《manuscripta mathematica》1999,100(3):277-289
We give a purely K-theoretic proof of a case of the “quantization commutes with reduction” result, conjectured by Guillemin and Sternberg and
proved by Meinrenken and Vergne. We show that the quantization is simply a pushforward in K-theory, and use Lerman's symplectic cutting and the localization theorem in equivariant K-theory to prove that quantization commutes with reduction. The case where G=S
1 and the action is free on the zero level set of the moment map is addressed.
Received: 9 March 1999 相似文献
2.
Let (G, K) be a Riemannian symmetric pair of maximal rank, where G is a compact simply connected Lie group and K is the fixed point set of an involutive automorphism σ. This induces an involutive automorphism τ of the based loop space Ω(G). There exists a maximal torus T ⊂ G such that the canonical action of T × S
1 on Ω(G) is compatible with τ (in the sense of Duistermaat). This allows us to formulate and prove a version of Duistermaat’s convexity theorem. Namely,
the images of Ω(G) and Ω(G)
τ
(fixed point set of τ) under the T × S
1 moment map on Ω(G) are equal. The space Ω(G)
τ
is homotopy equivalent to the loop space Ω(G/K) of the Riemannian symmetric space G/K. We prove a stronger form of a result of Bott and Samelson which relates the cohomology rings with coefficients in
\mathbbZ2 {\mathbb{Z}_2} of Ω(G) and Ω(G/K). Namely, the two cohomology rings are isomorphic, by a degree-halving isomorphism (Bott and Samelson [BS] had proved that the Betti numbers are equal). A version of this theorem involving equivariant cohomology is also proved.
The proof uses the notion of conjugation space in the sense of Hausmann, Holm, and Puppe [HHP]. 相似文献
3.
Jan Jaworowski 《Journal of Fixed Point Theory and Applications》2007,1(1):111-121
Suppose that G is a compact Lie group, M and N are orientable, free G-manifolds and f : M → N is an equivariant map. We show that the degree of f satisfies a formula involving data given by the classifying maps of the orbit spaces M/G and N/G. In particular, if the generator of the top dimensional cohomology of M/G with integer coefficients is in the image of the cohomology map induced by the classifying map for M, then the degree is one.
The condition that the map be equivariant can be relaxed: it is enough to require that it be “nearly equivariant”, up to a
positive constant. We will also discuss the G-average construction and show that the requirement that the map be equivariant can be replaced by a somewhat weaker condition
involving the average of the map.
These results are applied to maps into real, complex and quaternionic Stiefel manifolds. In particular, we show that a nearly
equivariant map of a complex or quaternionic Stiefel manifold into itself has degree one.
Dedicated to the memory of Jean Leray 相似文献
4.
We apply the “homotopy coniveau” machinery developed by the first-named author to the K-theory of coherent G-sheaves on a finite type G-scheme X over a field, where G is a finite group. This leads to a definition of G-equivariant higher Chow groups (different from the Chow groups of classifying spaces constructed by Totaro and generalized
to arbitrary X by Edidin–Graham) and an Atiyah–Hirzebruch spectral sequence from the G-equivariant higher Chow groups to the higher K-theory of coherent G-sheaves on X. This spectral sequence generalizes the spectral sequence from motivic cohomology to K-theory constructed by Bloch–Lichtenbaum and Friedlander–Suslin.
The first-named author gratefully acknowledges the support of the Humboldt Foundation through the Wolfgang Paul Program, and
support of the NSF via grants DMS-0140445 and DMS-0457195. 相似文献
5.
6.
Jinpeng An 《Geometriae Dedicata》2012,157(1):153-185
By using a Borel density theorem for algebraic quotients, we prove a theorem concerning isometric actions of a Lie group G on a smooth or analytic manifold M with a rigid A-structure σ. It generalizes Gromov’s centralizer and representation theorems to the case where R(G) is split solvable and G/R(G) has no compact factors, strengthens a special case of Gromov’s open dense orbit theorem, and implies that for smooth M and simple G, if Gromov’s representation theorem does not hold, then the local Killing fields on [(M)\tilde]{\widetilde{M}} are highly non-extendable. As applications of the generalized centralizer and representation theorems, we prove (1) a structural
property of Iso(M) for simply connected compact analytic M with unimodular σ, (2) three results illustrating the phenomenon that if G is split solvable and large then π
1(M) is also large, and (3) two fixed point theorems for split solvable G and compact analytic M with non-unimodular σ. 相似文献
7.
8.
Sorin Popa 《Inventiones Mathematicae》2006,165(2):409-451
We prove that any isomorphism θ:M0≃M of group measure space II1 factors,
,
, with G0 an ICC group containing an infinite normal subgroup with the relative property (T) of Kazhdan-Margulis (i.e. G0w-rigid) and σ a Bernoulli action of some ICC group G, essentially comes from an isomorphism of probability spaces which conjugates
the actions with respect to some identification G0≃G. Moreover, any isomorphism θ of M0 onto a “corner” pMp of M, for p∈M an idempotent, forces p=1. In particular, all group measure space factors associated with Bernoulli actions of w-rigid ICC groups have trivial fundamental
group and any isomorphism of such factors comes from an isomorphism of the corresponding groups. This settles a “group measure
space version” of Connes rigidity conjecture, shown in fact to hold true in a greater generality than just for ICC property
(T) groups. We apply these results to ergodic theory, establishing new strong rigidity and superrigidity results for orbit
equivalence relations. 相似文献
9.
Wang Yanming 《数学学报(英文版)》1991,7(1):62-65
By using the classification theorem of finite simple groups, we have shown that “IfG is a finite group,H is a coprime operator group ofG, C
G(H)≤S(G), thenG is solvable.” As a direct corollary, we have completely proved the long-standing conjecture on fixed-point-free automorphism
group.
The author is grateful to Professor Chen Zhongmu for his supervision. 相似文献
10.
Lowell Abrams 《Israel Journal of Mathematics》2000,117(1):335-352
The Poincaré duality of classical cohomology and the extension of this duality to quantum cohomology endows these rings with
the structure of a Frobenius algebra. Any such algebra possesses a canonical “characteristic element;” in the classical case
this is the Euler class, and in the quantum case this is a deformation of the classical Euler class which we call the “quantum
Euler class.” We prove that the characteristic element of a Frobenius algebraA is a unit if and only ifA is semisimple, and then apply this result to the cases of the quantum cohomology of the finite complex Grassmannians, and
to the quantum cohomology of hypersurfaces. In addition we show that, in the case of the Grassmannians, the [quantum] Euler
class equals, as [quantum] cohomology element and up to sign, the determinant of the Hessian of the [quantum] Landau-Ginzbug
potential. 相似文献
11.
Klaus Schmidt 《Israel Journal of Mathematics》1980,37(3):193-208
LetG be a countable group which acts non-singularly and ergodically on a Lebesgue space (X, ȑ, μ). A sequence (B
n) in ℒ is calledasymptotically invariant in lim
n
μ (B
nΔgB
n)=0 for everygεG. In this paper we show that the existence of such sequences can be characterized by certain simple assumptions on the cohomology
of the action ofG onX. As an explicit example we prove that a natural action of SL (2,Z) on the 2-sphere has no asymptotically invariant sequences. The last section deals with a particular cocycle for this action
which has an interpretation as a random walk on the integers with “time” in SL (2,Z). 相似文献
12.
R. Piergallini 《Commentarii Mathematici Helvetici》1992,67(1):287-292
We prove the following theorem: for any closed orientable 3-manifoldM and any homotopy 3-sphere Σ, there exists a simple 3-fold branched coveringp:M→Σ.
We also propose the conjecture that, for any primitive branched coveringp:M→N between orientable 3-manifolds,g(M)≥g(N), whereg denotes the Heegaard genus. By the above mentioned result, the genus 0 case of such conjecture is equivalent to the Poincaré
conjecture. 相似文献
13.
John R. Klein 《Mathematische Annalen》2001,319(3):421-456
To a topological group G, we assign a naive G-spectrum , called the dualizing spectrum of G. When the classifying space BG is finitely dominated, we show that detects Poincaré duality in the sense that BG is a Poincaré duality space if and only if is a homotopy finite spectrum. Secondly, we show that the dualizing spectrum behaves multiplicatively on certain topological
group extensions. In proving these results we introduce a new tool: a norm map which is defined for any G and for any naive G-spectrum E. Applications of the dualizing spectrum come in two flavors: (i) applications in the theory of Poincaré duality spaces, and
(ii) applications in the theory of group cohomology. On the Poincaré duality space side, we derive a homotopy theoretic solution
to a problem posed by Wall which says that in a fibration sequence of fini the total space satisfies Poincaré duality if and
only if the base and fiber do. The dualizing spectrum can also be used to give an entirely homotopy theoretic construction
of the Spivak fibration of a finitely dominated Poincaré duality space. We also include a new proof of Browder's theorem that
every finite H-space satisfies Poincaré duality. In connection with group cohomology, we show how to define a variant of Farrell-Tate cohomology
for any topological or discrete group G, with coefficients in any naive equivariant cohomology theory E. When E is connective, and when G admits a subgroup H of finite index such that BH is finitely dominated, we show that this cohomology coincides with the ordinary cohomology of G with coefficients in E in degrees greater than the cohomological dimension of H. In an appendix, we identify the homotopy type of for certain kinds of groups. The class includes all compact Lie groups, torsion free arithmetic groups and Bieri-Eckmann
duality groups.
Received July 14, 1999 / Revised May 17, 2000 / Published online February 5, 2001 相似文献
14.
We use techniques from homotopy theory, in particular the connection between configuration spaces and iterated loop spaces,
to give geometric explanations of stability results for the cohomology of the varieties of regular semisimple elements in
the simple complex Lie algebras of classical type A, B or C, as well as in the group . We show that the cohomology spaces of stable versions of these varieties have an algebraic stucture, which identifies them
as “free Poisson algebras” with suitable degree shifts. Using this, we are able to give explicit formulae for the corresponding
Poincaré series, which lead to power series identities by comparison with earlier work. The cases of type B and C involve ideas from equivariant homotopy theory. Our results may be interpreted in terms of the actions of a Weyl group on
its coinvariant algebra (i.e. the coordinate ring of the affine space on which it acts, modulo the invariants of positive
degree; this space coincides with the cohomology ring of the flag variety of the associated Lie group) and on the cohomology
of its associated complex discriminant variety.
Received August 31, 1998; in final form August 1, 1999 / Published online October 30, 2000 相似文献
15.
Wim Malfait 《manuscripta mathematica》1996,90(1):63-83
The main issue of this paper is the discussion of Nielsen’s realisation-problem for aspherical manifolds arising from (generalised)
Seifert fiber space constructions. We present sufficient conditions on such “model” aspherical manifoldsM to have that a finite abstract kernel ψ:G → Out (π1 (M)) can be (effectively) geometrically realised by a group of fiber preserving homeomorphisms ofM if and only if ψ can be realised by an (admissible) group extension 1 → (π1 (M)) →E’ →G → 1. Then an algebraic approach to a (partial) study of the symmetry ofM is possible. Our result covers all situations already described in literature and we show with an example that we also deal
with other types of Seifert fiber space constructions which were not yet treated before.
Research Assistant of the Belgian National Fund for Scientific Research (N.F.W.O.) 相似文献
16.
The M/G/K queueing system is one of the oldest models for multiserver systems and has been the topic of performance papers for almost
half a century. However, even now, only coarse approximations exist for its mean waiting time. All the closed-form (nonnumerical)
approximations in the literature are based on (at most) the first two moments of the job size distribution. In this paper
we prove that no approximation based on only the first two moments can be accurate for all job size distributions, and we
provide a lower bound on the inapproximability ratio, which we refer to as “the gap.” This is the first such result in the
literature to address “the gap.” The proof technique behind this result is novel as well and combines mean value analysis,
sample path techniques, scheduling, regenerative arguments, and asymptotic estimates. Finally, our work provides insight into
the effect of higher moments of the job size distribution on the mean waiting time. 相似文献
17.
The pre-coloring extension problem consists, given a graph G and a set of nodes to which some colors are already assigned, in finding a coloring of G with the minimum number of colors which respects the pre-coloring assignment. This can be reduced to the usual coloring problem
on a certain contracted graph. We prove that pre-coloring extension is polynomial for complements of Meyniel graphs. We answer
a question of Hujter and Tuza by showing that “PrExt perfect” graphs are exactly the co-Meyniel graphs, which also generalizes
results of Hujter and Tuza and of Hertz. Moreover we show that, given a co-Meyniel graph, the corresponding contracted graph
belongs to a restricted class of perfect graphs (“co-Artemis” graphs, which are “co-perfectly contractile” graphs), whose
perfectness is easier to establish than the strong perfect graph theorem. However, the polynomiality of our algorithm still
depends on the ellipsoid method for coloring perfect graphs.
C.N.R.S.
Final version received: January, 2007 相似文献
18.
Qiu Weisheng 《数学学报(英文版)》1994,10(1):49-58
The Multiplier Theorem is a celebrated theorem in the Design theory. The conditionp>λ is crucial to all known proofs of the multiplier theorem. However in all known examples of difference sets μ
p
. is a multiplier for every primep with (p, v)=1 andp‖n. Thus there is the multiplier conjecture: “The multiplier theorem holds without the assumption thatp>λ”. The general form of the multiplier theorem may be viewed as an attempt to partially resolve the multiplier conjecture,
where the assumption “p>λ” is replaced by “n
1>λ”. Since then Newman (1963), Turyn (1964), and McFarland (1970) attempted to partially resolve the multiplier conjecture
(see [7], [8], [9]). This paper will prove the following result using the representation theory of finite groups and the algebraic
number theory: LetG be an abelian group of orderv,v
0 be the exponent ofG, andD be a (v, k, λ)-difference set inG. Ifn=2n
1, then the general form of the multiplier theorem holds without the assumption thatn
1>λ in any of the following cases:
Supported by the scientific research finances of Peking University. 相似文献
2〈 | n 1; |
a | 2 Xn 1 and (v, 7)=1; |
2 Xn1, 7〈 | v, andt≡1 or 2 or 4 (mod 7). |
19.
Giuseppe Tomassini 《Milan Journal of Mathematics》2007,75(1):399-412
We deal with the general problem of extension of analytic objects in a complex space X. After a short presentation of the classical results we discuss some recent developments obtained when X is a semi-1-corona. Semi-1-coronae are domains C
+ whose boundary is the union of a Levi flat part, a 1-pseudoconvex part and a 1-pseudoconcave part. Using the main result
in [31], we prove a “bump lemma” for compact semi-1-coronae in and then, applying Andreotti-Grauert theory, we get a cohomology finiteness theorem for coherent sheaves whose depth is at
least 3. As an application we get an extension theorem for coherent sheaves and analytic subsets.
Received: April 2007 相似文献
20.
Let Γ be a tropical curve (or metric graph), and fix a base point p∈Γ. We define the Jacobian group J(G) of a finite weighted graph G, and show that the Jacobian J(Γ) is canonically isomorphic to the direct limit of J(G) over all weighted graph models G for Γ. This result is useful for reducing certain questions about the Abel–Jacobi map Φ
p
:Γ→J(Γ), defined by Mikhalkin and Zharkov, to purely combinatorial questions about weighted graphs. We prove that J(G) is finite if and only if the edges in each 2-connected component of G are commensurable over ℚ. As an application of our direct limit theorem, we derive some local comparison formulas between
ρ and
\varPhip*(r){\varPhi}_{p}^{*}(\rho) for three different natural “metrics” ρ on J(Γ). One of these formulas implies that Φ
p
is a tropical isometry when Γ is 2-edge-connected. Another shows that the canonical measure μ
Zh on a metric graph Γ, defined by S. Zhang, measures lengths on Φ
p
(Γ) with respect to the “sup-norm” on J(Γ). 相似文献