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1.
2.
We search for conditions on a countably compact (pseudocompact) topological semigroup under which: (i) each maximal subgroup
H(e) in S is a (closed) topological subgroup in S; (ii) the Clifford part H(S) (i.e. the union of all maximal subgroups) of the semigroup S is a closed subset in S; (iii) the inversion inv: H(S) → H(S) is continuous; and (iv) the projection π: H(S) → E(S), π: x ↦ xx
−1, onto the subset of idempotents E(S) of S, is continuous.
相似文献
3.
M. Akdağ 《Acta Mathematica Hungarica》2007,116(1-2):35-45
We define a multifunction F: X ⇝ Y to be upper (lower) D*-supercontinuous if F
+(V) (F
−(V)) is d*-open in X for every open set V of Y. We obtain some characterizations and several properties concerning upper (lower) D*-supercontinuous multifunctions.
相似文献
4.
Hans-Joachim Baues 《Inventiones Mathematicae》1998,132(3):467-489
5.
LetX be a 1-connected space with Moore loop space ΩX. By a well-known theorem of J. W. Milnor and J. C. Moore [7] the Hurewicz homomorphism induces an isomorphism of Hopf algebrasU(π*(ΩX) ⊗Q)→H
*(ΩX;Q). HereU(−) denotes the universal enveloping algebra and the Lie bracket on π*(ΩX) ⊗Q is given by the Samelson product.
Assume now thatX is the geometric realization of anr-reduced simplicial set,r≥3. LetL
X
be a differential graded free Lie algebra over ℤ describing the tame homotopy type ofX according to the theory of [4]. Then the main result of the present paper is the construction of a sequence of morphisms
of differential graded algebras betwenU(L
X
) and the algebraC U
*(ΩX)z of normalized cubical chains on ΩX such that the induced morphisms on homology with coefficientsR
k
are isomorphismsH
r-1+l
(U(L
x
);R
k
) ≅H
r-1+l
C U
*(ΩX);R
k
) forl≤k; hereR
0⊆R
1⊆… is a tame ring system, i. e.R
k
)⊑Q and each primep with 2p−3≤k is invertible inR
k
.
However, it is no longer true that the Pontrjagin algebraH
≤r−1+k
(ΩX; R
k
) of ΩX in degrees ≤r−1+k is determined by π*(ΩX) or by a cofibrant (-fibrant) modelM of π*(ΩX) as will be shown by an example. But there is a filtration onH
≤r−1+k
(ΩX; R
k
) such that the associated graded algebra is isomorphic toH
≤r−1+k
(U(M); R
k
).This will be proved by using a filtered Lie algebra model ofX constructed from a bigraded model of π*(ΩX).
Supported by a CNRS grant and PROCOPE
Supported by PROCOPE 相似文献
6.
Palanivel Manoharan 《manuscripta mathematica》2008,125(1):127-137
For a fibre preserving map ϕ: E → E on a fibration (E, π, B), we construct a grading preserving map T(ϕ, π) between H*(E) and H*(B) that generalizes the Lefschetz number. If T(ϕ, π) is an isomorphism between H
0(E) and H
0(B), then π restricts to a surjective local diffeomorphism on each connected component of the fixed point set of ϕ under a transversality condition. This yields a characterization for the bundle H → G → G/H to be trivial when π
1 (G/H) = 0. 相似文献
7.
Guyan Robertson 《K-Theory》2004,33(4):347-369
Let (G, I, N, S) be an affine topological Tits system, and let Γ be a torsion-free cocompact lattice in G. This article studies the coinvariants H
0(Γ; C(Ω,Z)), where Ω is the Furstenberg boundary of G. It is shown that the class [1] of the identity function in H
0(Γ; C(Ω, Z)) has finite order, with explicit bounds for the order. A similar statement applies to the K
0 group of the boundary crossed product C
*-algebra C(Ω)Γ. If the Tits system has type ?
2, exact computations are given, both for the crossed product algebra and for the reduced group C
*-algebra. 相似文献
8.
For natural numbers r,s,q,m,n with s≥r≤q we determine all natural functions g: T
*(J
(r,s,q)(Y, R
1,1)0)*→R for any fibered manifold Y with m-dimensional base and n-dimensional fibers. For natural numbers r,s,m,n with s≥r we determine all natural functions g: T
*(J
(r,s)
(Y, R)0)*→R for any Y as above. 相似文献
9.
Imre Patyi 《Mathematische Annalen》2003,326(3):443-458
Let X be one of the Banach spaces c
0
, ℓ
p
, 1≤p<∞; Ω⊂X pseudoconvex open, a holomorphic Banach vector bundle with a Banach Lie group G
*
for structure group. We show that a suitable Runge-type approximation hypothesis on X, G
*
(which we also prove for G
*
a solvable Lie group) implies the vanishing of the sheaf cohomology groups H
q
(Ω, 𝒪
E
), q≥1, with coefficients in the sheaf of germs of holomorphic sections of E. Further, letting 𝒪Γ (𝒞Γ) be the sheaf of germs of holomorphic (continuous) sections of a Banach Lie group bundle Γ→Ω with Banach Lie groups G, G
*
for fiber group and structure group, we show that a suitable Runge-type approximation hypothesis on X, G, G
*
(which we prove again for G, G
*
solvable Lie groups) implies the injectivity (and for X=ℓ1 also the surjectivity) of the Grauert–Oka map H
1
(Ω, 𝒪Γ)→H
1
(Ω, 𝒞Γ) of multiplicative cohomology sets.
Received: 1 March 2002 /
Published online: 28 March 2003
Mathematics Subject Classification (2000): 32L20, 32L05, 46G20
RID="*"
ID="*" Kedves Laci Móhan kisfiamnak.
RID="*"
ID="*" To my dear little Son 相似文献
10.
Given a map f: X→Y and a Nielsen root class, there is a number associated to this root class, which is the minimal number of points among all
root classes which are H-related to the given one for all homotopies H of the map f. We show that for maps between closed surfaces it is possible to deform f such that all the Nielsen root classes have cardinality equal to the minimal number if and only if either N R[f]≤1, or N R[f]>1 and f satisfies the Wecken property. Here N R[f] denotes the Nielsen root number. The condition “f satisfies the Wecken property is known to be equivalent to |deg(f)|≤N R[f]/(1−χ(M
2)−χ(M
10/(1−χ(M
2)) for maps between closed orientable surfaces. In the case of nonorientable surfaces the condition is A(f)≤N R[f]/(1−χ(M
2)−χ(M
2)/(1−χ(M
2)). Also we construct, for each integer n≥3, an example of a map f: K
n
→N from an n-dimensionally connected complex of dimension n to an n-dimensional manifold such that we cannot deform f in a way that all the Nielsen root classes reach the minimal number of points at the same time. 相似文献
11.
Subhash J. Bhatt 《Proceedings Mathematical Sciences》2006,116(2):161-173
Given anm-tempered strongly continuous action α of ℝ by continuous*-automorphisms of a Frechet*-algebraA, it is shown that the enveloping ↡-C
*-algebraE(S(ℝ, A∞, α)) of the smooth Schwartz crossed productS(ℝ,A
∞, α) of the Frechet algebra A∞ of C∞-elements ofA is isomorphic to the Σ-C
*-crossed productC
*(ℝ,E(A), α) of the enveloping Σ-C
*-algebraE(A) ofA by the induced action. WhenA is a hermitianQ-algebra, one getsK-theory isomorphismRK
*(S(ℝ, A∞, α)) =K
*(C
*(ℝ,E(A), α) for the representableK-theory of Frechet algebras. An application to the differential structure of aC
*-algebra defined by densely defined differential seminorms is given. 相似文献
12.
Guizhen LIU 《Frontiers of Mathematics in China》2009,4(2):311-323
Let G be a digraph with vertex set V(G) and arc set E(G) and let g = (g
−, g
+) and ƒ = (ƒ
−, ƒ
+) be pairs of positive integer-valued functions defined on V(G) such that g
−(x) ⩽ ƒ
−(x) and g
+(x) ⩽ ƒ
+(x) for each x ∈ V(G). A (g, ƒ)-factor of G is a spanning subdigraph H of G such that g
−(x) ⩽ id
H
(x) ⩽ ƒ
−(x) and g
+(x) ⩽ od
H
(x) ⩽ ƒ
+(x) for each x ∈ V(H); a (g, ƒ)-factorization of G is a partition of E(G) into arc-disjoint (g, ƒ)-factors. Let
= {F
1, F
2,…, F
m} and H be a factorization and a subdigraph of G, respectively.
is called k-orthogonal to H if each F
i
, 1 ⩽ i ⩽ m, has exactly k arcs in common with H. In this paper it is proved that every (mg+m−1,mƒ−m+1)-digraph has a (g, f)-factorization k-orthogonal to any given subdigraph with km arcs if k ⩽ min{g
−(x), g
+(x)} for any x ∈ V(G) and that every (mg, mf)-digraph has a (g, f)-factorization orthogonal to any given directed m-star if 0 ⩽ g(x) ⩽ f(x) for any x ∈ V(G). The results in this paper are in some sense best possible.
相似文献
13.
Let X be a normed space that satisfies the Johnson–Lindenstrauss lemma (J–L lemma, in short) in the sense that for any integer
n and any x
1,…,x
n
∈X, there exists a linear mapping L:X→F, where F⊆X is a linear subspace of dimension O(log n), such that ‖x
i
−x
j
‖≤‖L(x
i
)−L(x
j
)‖≤O(1)⋅‖x
i
−x
j
‖ for all i,j∈{1,…,n}. We show that this implies that X is almost Euclidean in the following sense: Every n-dimensional subspace of X embeds into Hilbert space with distortion
22O(log*n)2^{2^{O(\log^{*}n)}}
. On the other hand, we show that there exists a normed space Y which satisfies the J–L lemma, but for every n, there exists an n-dimensional subspace E
n
⊆Y whose Euclidean distortion is at least 2Ω(α(n)), where α is the inverse Ackermann function. 相似文献
14.
Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum σπ (T) of T is defined by σπ (T) = z ∈ σ(T): |z| = maxw∈σ(T) |w|. If surjective (not necessarily linear nor continuous) maps φ, ϕ: A → B satisfy σπ (φ(S)ϕ(T)) = σπ (ST) for all S; T ∈ A, then φ and ϕ are either of the form φ(T) = A
1
TA
2
−1 and ϕ(T) = A
2
TA
1
−1 for some bijective bounded linear operators A
1; A
2 of X onto Y, or of the form φ(T) = B
1
T*B
2
−1 and ϕ(T) = B
2
T*B
−1 for some bijective bounded linear operators B
1;B
2 of X* onto Y.
相似文献
15.
Fu Qing GAO 《数学学报(英文版)》2007,23(8):1527-1536
Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E(X1) and let {N(t); t ≥0} be a random process taking non-negative integer values with finite mean λ(t) = E(N(t)) and independent of {Xn; n ≥1}. In this paper, asymptotic expressions of P((X1 +… +XN(t)) -λ(t)μ 〉 x) uniformly for x ∈[γb(t), ∞) are obtained, where γ〉 0 and b(t) can be taken to be a positive function with limt→∞ b(t)/λ(t) = 0. 相似文献
16.
Xiao Hong Fu 《数学学报(英文版)》2008,24(9):1475-1482
This paper considers the isometric extension problem concerning the mapping from the unit sphere S
1(E) of the normed space E into the unit sphere S
1(l
∞(Γ)). We find a condition under which an isometry from S
1(E) into S
1(l
∞(Γ)) can be linearly and isometrically extended to the whole space. Since l
∞(Γ) is universal with respect to isometry for normed spaces, isometric extension problems on a class of normed spaces are
solved. More precisely, if E and F are two normed spaces, and if V
0: S
1(E) → S
1(F) is a surjective isometry, where c
00(Γ) ⊆ F ⊆ l
∞(Γ), then V
0 can be extended to be an isometric operator defined on the whole space.
This work is supported by Natural Science Foundation of Guangdong Province, China (Grant No. 7300614) 相似文献
17.
Let F be a non-Archimedean local field whose residue characteristic is odd. In this paper we develop a theory of newforms
forU (1, 1)(F), building on previous work onSL
2(F). This theory is analogous to the results of Casselman forGL
2(F) and Jacquet, Piatetski-Shapiro, and Shalika forGL
n(F). To a representation π ofU(1, 1)(F), we attach an integer c(π) called the conductor of π, which depends only on theL-packet π containing π. A newform is a vector in π which is essentially fixed by a congruence subgroup of level c(π). We show
that our newforms are always test vectors for some standard Whittaker functionals, and, in doing so, we give various explicit
formulae for newforms. 相似文献
18.
Philippe Bonnet 《manuscripta mathematica》2003,110(4):413-432
Let F be a polynomial mapping from ℂ
n
to ℂ
q
with n>q. We study the De Rham cohomology of its fibres and its relative cohomology groups, by introducing a special fibre F
−1(∞) ``at infinity' and its cohomology. Let us fix a weighted homogeneous degree on with strictly positive weights. The fibre at infinity is the zero set of the leading terms of the coordinate functions of
F. We introduce the cohomology groups H
k
(F
−1(∞)) of F at infinity. These groups enable us to compute all the other cohomology groups of F. For instance, if the fibre at infinity has an isolated singularity at the origin, we prove that every weighted homogeneous
basis of H
n−q
(F
−1
(∞)) is a basis of all the groups H
n−q
(F
−1(y)) and also a basis of the (n−q)
th
relative cohomology group of F. Moreover the dimension of H
n−q
(F
−1(∞)) is given by a global Milnor number of F, which only depends on the leading terms of the coordinate functions of F.
Received: 12 February 2002 / Revised version: 25 May 2002 Published online: 3 March 2003 相似文献
19.
Mikhail Gromov 《Geometric And Functional Analysis》2010,20(2):416-526
We find lower bounds on the topology of the fibers F-1(y) ì X{F^{-1}(y)\subset X} of continuous maps F : X → Y in terms of combinatorial invariants of certain polyhedra and/or of the cohomology algebras H*(X). Our exposition is conceptually related to but essentially independent of Part 1 of the paper. 相似文献
20.
David Mejzler 《Israel Journal of Mathematics》1987,57(1):1-27
LetX
1, ...,X
n be independent random variables, letF
i be the distribution function ofX
i (1≦i≦n) and letX
1n
≦... ≦X
nn be the corresponding order statistics. We consider the statisticsX
kn, wherek=k(n),k/n → 1 andn−k → ∞. Under some additional restrictions concerning the behaviour of the sequences {a
n>0,b
n,k(n),F
n} we characterize the class of all distribution functionsH such that Prob{(X
kn
−b
n
)/a
n
<x)}→H.
Dedicated to the Memory of N. V. Smirnov (1900–1966) 相似文献