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1.
Let be the kernel of the natural map Out(Fn)→GLn(ℤ). We use combinatorial Morse theory to prove that has an Eilenberg–MacLane space which is (2n-4)-dimensional and that is not finitely generated (n≥3). In particular, this shows that the cohomological dimension of is equal to 2n-4 and recovers the result of Krstić–McCool that is not finitely presented. We also give a new proof of the fact, due to Magnus, that is finitely generated. 相似文献
2.
Emanuele Delucchi 《Journal of Algebraic Combinatorics》2007,26(4):477-494
Given a finite group G and a natural number n, we study the structure of the complex of nested sets of the associated Dowling lattice
(Proc. Internat. Sympos., 1971, pp. 101–115) and of its subposet of the G-symmetric partitions
which was recently introduced by Hultman (, 2006), together with the complex of G-symmetric phylogenetic trees
. Hultman shows that the complexes
and
are homotopy equivalent and Cohen–Macaulay, and determines the rank of their top homology.
An application of the theory of building sets and nested set complexes by Feichtner and Kozlov (Selecta Math. (N.S.)
10, 37–60, 2004) shows that in fact
is subdivided by the order complex of
. We introduce the complex of Dowling trees
and prove that it is subdivided by the order complex of
. Application of a theorem of Feichtner and Sturmfels (Port. Math. (N.S.)
62, 437–468, 2005) shows that, as a simplicial complex,
is in fact isomorphic to the Bergman complex of the associated Dowling geometry.
Topologically, we prove that
is obtained from
by successive coning over certain subcomplexes. It is well known that
is shellable, and of the same dimension as
. We explicitly and independently calculate how many homology spheres are added in passing from
to
. Comparison with work of Gottlieb and Wachs (Adv. Appl. Math.
24(4), 301–336, 2000) shows that
is intimely related to the representation theory of the top homology of
.
Research partially supported by the Swiss National Science Foundation, project PP002-106403/1. 相似文献
3.
Vladimir Markovic 《Inventiones Mathematicae》2007,168(3):523-566
In this paper, we show that the mapping class group of a closed surface can not be geometrically realized as a group of homeomorphisms
of that surface. More precisely, let denote the standard projection of the group of homeomorphisms to the mapping class group of a closed surface M of genus g>5. We show that there is no homomorphism , such that is the identity. This answers a question by Thurston (see [11]).
Mathematics Subject Classification (2000) Primary 20H10, 37F30 相似文献
4.
We calculate the E-polynomials of certain twisted GL(n,ℂ)-character varieties of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example,
the value of the topological Euler characteristic of the associated PGL(n,ℂ)-character variety. The calculation also leads to several conjectures about the cohomology of : an explicit conjecture for its mixed Hodge polynomial; a conjectured curious hard Lefschetz theorem and a conjecture relating
the pure part to absolutely indecomposable representations of a certain quiver. We prove these conjectures for n=2. 相似文献
5.
Béatrice Vedel 《Journal of Fourier Analysis and Applications》2009,15(1):101-123
We propose the construction of wavelet bases with pseudo-polynomials adapted to the homogeneous Sobolev spaces
, s−n/2∈ℕ. They provide a confinement of the infrared divergence by decomposing
as a direct sum X
⊕
Y where X is a “small” space which carries the divergence and Y can be embedded in
. In the case of
we also construct such an orthonormal basis, which provides a confinement of the Mumford process. 相似文献
6.
Luigi Santocanale 《Order》2007,24(3):155-179
7.
Hendrik Hubrechts 《Foundations of Computational Mathematics》2008,8(1):137-169
Let E
Γ be a family of hyperelliptic curves defined by
, where
is defined over a small finite field of odd characteristic. Then with
in an extension degree n field over this small field, we present a deterministic algorithm for computing the zeta function of the curve
by using Dwork deformation in rigid cohomology. The time complexity of the algorithm is
and it needs
bits of memory. A slight adaptation requires only
space, but costs time
. An implementation of this last result turns out to be quite efficient for n big enough.
H. Hubrechts is a Research Assistant of the Research Foundation–Flanders (FWO–Vlaanderen). 相似文献
8.
In the study of the asymptotic behaviour of solutions of differential-difference equations the
-spectrum has been useful, where
and
implies Fourier transform
, with
given
, φ∈L
∞(ℝ,X), X a Banach space,
(half)line. Here we study
and related concepts, give relations between them, especially
weak Laplace half-line spectrum of φ, and thus ⊂ classical Beurling spectrum = Carleman spectrum =
; also
= Beurling spectrum of “φ modulo
” (Chill-Fasangova). If
satisfies a Loomis type condition (L
U
), then
countable and
uniformly continuous ∈U are shown to imply
; here (L
U
) usually means
, indefinite integral Pf of f in U imply Pf in
(the Bohl-Bohr theorem for
= almost periodic functions, U=bounded functions). This spectral characterization and other results are extended to unbounded functions via mean classes
, ℳ
m
U ((2.1) below) and even to distributions, generalizing various recent results for uniformly continuous bounded φ. Furthermore for solutions of convolution systems S*φ=b with
in some
we show
. With these above results, one gets generalizations of earlier results on the asymptotic behaviour of solutions of neutral
integro-differential-difference systems. Also many examples and special cases are discussed. 相似文献
9.
J. Bagherian Ilia Ponomarenko A. Rahnamai Barghi 《Journal of Algebraic Combinatorics》2008,27(2):173-185
We introduce a concept of cyclotomic association scheme over a finite near-field
. It is proved that any isomorphism of two such nontrivial schemes is induced by a suitable element of the group AGL(V), where V is the linear space associated with
. A sufficient condition on a cyclotomic scheme
that guarantee the inclusion
where
is a finite field with
elements, is given.
I. Ponomarenko partially supported by RFFI, grants 03-01-00349, NSH-2251.2003.1. 相似文献
10.
We describe the Chow ring with rational coefficients of as the subring of invariants of a ring , relative to the action of the group of symmetries Sd. We compute by following a sequence of intermediate spaces for . 相似文献
11.
Tomoyuki Arakawa 《Inventiones Mathematicae》2007,169(2):219-320
We study the representation theory of the -algebra associated with a simple Lie algebra at level k. We show that the “-” reduction functor is exact and sends an irreducible module to zero or an irreducible module at any
level k∈ℂ. Moreover, we show that the character of each irreducible highest weight representation of is completely determined by that of the corresponding irreducible highest weight representation of affine Lie algebra of . As a consequence we complete (for the “-” reduction) the proof of the conjecture of E. Frenkel, V. Kac and M. Wakimoto on
the existence and the construction of the modular invariant representations of -algebras.
Mathematics Subject Classification (1991) 17B68, 81R10 相似文献
12.
A. Gerlo 《Applied Categorical Structures》2008,16(4):479-493
In a topological construct endowed with a proper -factorization system and a concrete functor , we study -compactness and -Hausdorff separation, where is a class of “closed morphisms” in the sense of Clementino et al. (A functional approach to general topology. In: Categorical
Foundations. Encyclopedia of Mathematics and Its Applications, vol. 97, pp. 103–163. Cambridge University Press, Cambridge,
2004), determined by Λ. In particular, we point out under which conditions on Λ, the notion of -compactness of an object of coincides with 0-compactness of the image in Prap. Our results will be illustrated by some examples: except for some well-known ones, like b-compactness of a topological space, we also capture some compactness notions that were not considered before in the literature.
In particular, we obtain a generalization of b-compactness to the setting of approach spaces. This notion is shown to play an important role in the study of uniformizability.
The author is research assistant at the Fund of Scientific Research Vlaanderen (FWO). 相似文献
13.
Bent functions have many applications in the fields of coding theory, communications and cryptography. This paper studies
the constructions of bent functions having the form
for odd n and
for even n, over the finite field
of odd characteristic p, where
. Based on the irreducibility of some polynomials on
, we focus on characterizing the bent functions for n=p
v
q
r
and n=2p
v
q
r
, where
is an odd prime and p a primitive root modulo q
2. Moreover, the enumerations of those functions are also considered.
Partially supported by the NSF of China under Grants No. 60603012 and No. 60573053. 相似文献
14.
Let denote the set of simultaneously - approximable points in and denote the set of multiplicatively ψ-approximable points in . Let be a manifold in . The aim is to develop a metric theory for the sets and analogous to the classical theory in which is simply . In this note, we mainly restrict our attention to the case that is a planar curve . A complete Hausdorff dimension theory is established for the sets and . A divergent Khintchine type result is obtained for ; i.e. if a certain sum diverges then the one-dimensional Lebesgue measure on of is full. Furthermore, in the case that is a rational quadric the convergent Khintchine type result is obtained for both types of approximation. Our results for
naturally generalize the dimension and Lebesgue measure statements of Beresnevich et al. (Mem AMS, 179 (846), 1–91 (2006)). Moreover, within the multiplicative framework, our results for constitute the first of their type.
The research of Victor V. Beresnevich was supported by an EPSRC Grant R90727/01. Sanju L. Velani is a Royal Society University
Research Fellow.
For Iona and Ayesha on No. 3. 相似文献
15.
Sorin Popa 《Inventiones Mathematicae》2007,170(2):243-295
We prove that if a countable discrete group Γ is w-rigid, i.e. it contains an infinite normal subgroup H with the relative property (T) (e.g. , or Γ=H×H’ with H an infinite Kazhdan group and H’ arbitrary), and is a closed subgroup of the group of unitaries of a finite separable von Neumann algebra (e.g. countable discrete, or separable compact), then any -valued measurable cocycle for a measure preserving action of Γ on a probability space (X,μ) which is weak mixing on H and s-malleable (e.g. the Bernoulli action ) is cohomologous to a group morphism of Γ into . We use the case discrete of this result to prove that if in addition Γ has no non-trivial finite normal subgroups then any orbit equivalence
between and a free ergodic measure preserving action of a countable group Λ is implemented by a conjugacy of the actions, with respect
to some group isomorphism Γ≃Λ. 相似文献
16.
Rolf Farnsteiner 《Inventiones Mathematicae》2006,166(1):27-94
Given an algebraically closed field k of characteristic p≥3, we classify the finite algebraic k-groups whose algebras of measures afford a principal block of tame representation type. The structure of such a group
is largely determined by a linearly reductive subgroup scheme
of SL(2), with the McKay quiver of
relative to its standard module being the Gabriel quiver of the principal block
. The graphs underlying these quivers are extended Dynkin diagrams of type
or
, and the tame blocks are Morita equivalent to generalizations of the trivial extensions of the radical square zero tame hereditary
algebras of the corresponding type. 相似文献
17.
We prove the existence of equivariant finite time blow-up solutions for the wave map problem from ℝ2+1→S
2 of the form where u is the polar angle on the sphere, is the ground state harmonic map, λ(t)=t
-1-ν, and is a radiative error with local energy going to zero as t→0. The number can be prescribed arbitrarily. This is accomplished by first “renormalizing” the blow-up profile, followed by a perturbative
analysis.
Mathematics Subject Classification (1991) 35L05, 35Q75, 35P25 相似文献
18.
Sascha Orlik 《Inventiones Mathematicae》2008,172(3):585-656
Let be Drinfeld’s upper half space over a finite extension K of ℚ
p
. We construct for every GL
d+1-equivariant vector bundle on ℙ
d
K
, a GL
d+1(K)-equivariant filtration by closed subspaces on the K-Fréchet . This gives rise by duality to a filtration by locally analytic GL
d+1(K)-representations on the strong dual . The graded pieces of this filtration are locally analytic induced representations from locally algebraic ones with respect
to maximal parabolic subgroups. This paper generalizes the cases of the canonical bundle due to Schneider and Teitelbaum [ST1]
and that of the structure sheaf by Pohlkamp [P]. 相似文献
19.
D. Caro 《Inventiones Mathematicae》2007,170(3):507-539
Résumé Soient un anneau de valuation discrète complet d’inégales caractéristiques, de corps résiduel parfait k, un -schéma formel propre et lisse, T un diviseur de la fibre spéciale P de , U l’ouvert de P complémentaire de T, Y un sous-k-schéma fermé lisse de U. Nous prouvons que la catégorie des F-isocristaux surconvergents sur Y est équivalente à celle des F-isocristaux surcohérents sur Y (voir [Car, 6.2.1 et 6.4.3.a)]). Plus généralement, nous établissons par recollement une telle équivalence pour tout k-schéma séparé lisse Y. Nous vérifions de plus que les F-complexes de -modules à cohomologie bornée et -surcohérente se dévissent en F-isocristaux surconvergents. 相似文献
20.
For a smooth curve C it is known that a very ample line bundle on C is normally generated if Cliff() < Cliff(C) and there exist extremal line bundles (:non-normally generated very ample line bundle with Cliff() = Cliff(C)) with . However it has been unknown whether there exists an extremal line bundle with . In this paper, we prove that for any positive integers (g, c) with g = 2c + 5 and (mod 2) there exists a smooth curve of genus g and Clifford index c carrying an extremal line bundle with . In fact, a smooth quadric hypersurface section C of a general projective K3 surface always has an extremal line bundle with . More generally, if C has a line bundle computing the Clifford index c of C with , then C has such an extremal line bundle .
For all authors, this work was supported by Korea Research Foundation Grant funded by Korea Government (MOEHRD, Basic Reasearch
Promotion Fund)(KRF-2005-070-C00005). 相似文献