定向Hantzsche-Wendt流形的上同调刚度
Cohomological rigidity of oriented Hantzsche-Wendt manidolds
摘要：
通过Hantzsche-Wendt流形（简称HW-流形），我们可以理解任何具有和乐群（Z_2）^{n-1}的n维定向闭黎曼流形。两个HW-流形M_1和M_2是上同调刚性的当且仅当M_1和M_2之间的同胚映射等价于分次环H^{*}（M_1，F_2）和H^{*}（M_2，F_2）的同构。证明了HW-流形是上同调刚性的。
英文摘要：
By Hantzsche-Wendt manifold (for short HW-manifold) we understand any oriented closed Riemannian manifold of dimension n with a holonomy group (Z_2)^{n-1}. Two HW-manifolds M_1 and M_2 are cohomological rigid if and only if a homeomorphism between M_1 and M_2 is equivalent to an isomorphism of graded rings H^{*}(M_1,F_2) and H^{*}(M_2,F_2). We prove that HW-manifolds are cohomological rigid.
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