Coarse Alexander对偶与对偶群
Coarse Alexander duality and duality groups
摘要：
本文研究了粗糙Poincare对偶空间上的离散群作用，例如非循环单纯复形允许Poincare对偶群的自由余紧群作用.当G是一个n-1维对偶群，X是一个形式维数为n的粗Poincare对偶空间时，G在X上的一个自由单纯作用决定了一个“外围”子群F_1，. F_k，使得群对（G;F_1，.，F_k）是一个n维Poincare对偶对。特别地，如果G是FP_2型的2维1-端群，X是粗PD（3）空间，则G包含曲面子群;如果X是单连通的，则得到Scott/Shalen紧核定理在粗PD（3）空间上的部分推广.
英文摘要：
We study discrete group actions on coarse Poincare duality spaces, e.g. acyclic simplicial complexes which admit free cocompact group actions by Poincare duality groups. When G is an (n-1) dimensional duality group and X is a coarse Poincare duality space of formal dimension n, then a free simplicial action of G on X determines a collection of ``peripheral'' subgroups F_1,...,F_k in G so that the group pair (G;F_1,...,F_k) is an n-dimensional Poincare duality pair. In particular, if G is a 2-dimensional 1-ended group of type FP_2, and X is a coarse PD(3) space, then G contains surface subgroups; if in addition X is simply connected, then we obtain a partial generalization of the Scott/Shalen compact core theorem to the setting of coarse PD(3) spaces.
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