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1.
A small cover is a closed manifold $M^{n}$ with a locally standard
$(\Bbb{Z}_{2})^{n}$-action such that its orbit space is a simple
convex polytope $P^{n}$. Let $\Delta^{n}$ denote an $n$-simplex and
$P(m)$ an $m$-gon. This paper gives formulas for calculating the
number of D-J equivalent classes and equivariant homeomorphism
classes of orientable small covers over the product space
$\Delta^{n_1}\times \Delta^{n_2} \times P(m)$, where $n_1$ is odd. 相似文献
2.
《数学年刊B辑(英文版)》2016,(3)
A small cover is a closed manifold M~n with a locally standard(Z_2)~n-action such that its orbit space is a simple convex polytope P~n. Let Δ~n denote an n-simplex and P(m) an m-gon. This paper gives formulas for calculating the number of D-J equivalent classes and equivariant homeomorphism classes of orientable small covers over the product space Δ~(n_1)×Δ~(n_2)× P(m), where n_1 is odd. 相似文献
3.
In this paper,it is shown that for a 3-dimensional small cover M over a polytope P,there are only 2-torsions in H1(M;Z).Moreover,the mod 2 Betti number growth of finite covers of M is studied. 相似文献
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5.
Shintar?o KUROKI 《数学年刊B辑(英文版)》2010,31(3):393-410
The purpose of this paper is to study relations among equivariant operations on 3-dimensional small covers. The author gets three formulas for these operations. As an application, the Nishimura's theorem on the construction of oriented 3-dimensional small covers and the Lu-Yu's theorem on the construction of all 3-dimensional small covers are improved. Moreover, for a construction of 3-dimensional 2-torus manifolds, it is shown that all operations can be obtained by using the equivariant surgeries. 相似文献
6.
Zhangmin HUANG 《数学年刊B辑(英文版)》2020,41(2):163-176
Let π : Mn→Pn be an n-dimensional small cover over Pn and λ : F(Pn)→Z2n be its characteristic function. The author uses the symbol c(λ) to denote the cardinal number of the image Im(λ). If c(λ) = n + 1 or n + 2, then a necessary and sufficient condition on the existence of spin structure on Mnis given. As a byproduct, under some special conditions, the author uses the second Stiefel-Whitney class to detect when Pn is n-... 相似文献
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Erwann Delay 《Advances in Mathematics》2002,168(2):213-224
On an asymptotically hyperbolic Einstein manifold (M,g0) for which the Yamabe invariant of the conformal structure on the boundary at infinity is nonnegative, we show that the operators of Ricci curvature, and of Einstein curvature, are locally invertible in a neighborhood of the metric g0. We deduce in the C∞ case that the image of the Riemann-Christoffel curvature operator is a submanifold in a neighborhood of g0. 相似文献
9.
Mathematical Notes - 相似文献
10.
We compute the Betti numbers of two-fold coverings of small covers with some special properties; in particular, we use the results of Davis and Januszkiewicz on the cohomology of small covers. It turned out that their proof contains some gap that we describe in detail and fill in. 相似文献
11.
Patrick Bernard 《Annales Henri Poincare》2010,11(5):929-942
We prove the existence of normally hyperbolic cylinders in a priori stable Hamiltonian systems the size of which is bounded from below independently of the size of the perturbation. This result should have applications to the study of Arnold’s diffusion. 相似文献
12.
Siberian Mathematical Journal - 相似文献
13.
We prove a global existence result for a semilinear degenerate hyperbolic Cauchyproblem with large data, in the case ofa subcritical defocusing power nonlinearity, in 1 and 2 space dimensions. 相似文献
14.
多面体上的小覆盖的等变配边类是由它的切表示集所决定的.本文通过将棱柱上的小覆盖的切表示集约化到一种素形式,来确定其等变配边分类. 相似文献
15.
We apply a construction of Rips to show that a number of algorithmicproblems concerning certain small cancellation groups and, inparticular, word hyperbolic groups, are recursively unsolvable.Given any integer k > 2, there is no algorithm to determinewhether or not any small cancellation group can be generatedby either two elements or more than k elements. There is a smallcancellation group E such that there is no algorithm to determinewhether or not any finitely generated subgroup of E is all ofE, or is finitely presented, or has a finitely generated secondintegral homology group. 相似文献
16.
Deng Pin Liu 《数学学报(英文版)》2018,34(11):1742-1754
Let Pn be a simple n-polytope with a Z2-characteristic function λ. And h is a Morse function over Pn. Then the small cover Mn(λ) corresponding to the pair (Pn, λ) has a cell structure given by h. From this cell structure we can derive a cellular chain complex of Mn(λ) with integer coefficients. In this paper, firstly, we discuss the highest dimensional boundary morphism ∂n of this cellular chain complex and get that ∂n=0 or 2 by a natural way. And then, from the well-known result that the submanifold corresponding to (F, λF) is naturally a small cover with dimension k, where F is any k-face of Pn and λF is the restriction of λ on F, we get that ∂k=0 or ±2 for 0 ≤ k < n. Finally, by using the definition of inherited characteristic function which is the restriction of λ on the faces of Pn, we get a way to calculate the homology groups of Mn(λ). Applying our result to a 3-small cover we have that the homology groups of any 3-small cover is torsion-free or has only 2-torsion. 相似文献
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Daniele Angella 《Journal of Geometric Analysis》2013,23(3):1355-1378
We prove that, for some classes of complex nilmanifolds, the Bott–Chern cohomology is completely determined by the Lie algebra associated with the nilmanifold with the induced complex structure. We use these tools to compute the Bott–Chern and Aeppli cohomologies of the Iwasawa manifold and of its small deformations, completing the computations by M. Schweitzer (arXiv:0709.3528v1 [math.AG]). 相似文献
19.
付鑫 《数学年刊A辑(中文版)》2017,38(2):227-242
计算了L\"{o}bell多面体上的小覆盖的等变微分同胚类的个数.
在1991年, Davis和Januszkiewicz提出了小覆盖的概念,
给出了组合和拓扑间的一种直接联系,
并证明了单凸多面体上的特征映射($\mathbb{Z}_2^n$染色)与该多面体上的小覆盖一一对应.
文中作者给出了L\"{o}bell多面体上的自同构群和染色规律,
结合Burnside引理计算了一般的L\"{o}bell多面体上的小覆盖的等变微分同胚类的个数. 相似文献
20.
令G为一具有n个节点的平面近三角剖分图,C为G的一个少圈二重覆盖(SCDC).本文首先给出了G的一些生成元,由此可以得到G的一个SCDC.若G为一外平面近三角剖分图,得到 |C|≤n-2的一充分必要条件;若 G至少有一个内点,得到|C|≤n-2的一充分条件. 相似文献