Duality and invariants for Butler groups

New Invariants for Groups

5 Groups 21 5.1 Chains arising from abelianising functions . . . . . . . . . . . . . 21 5.2 Low-dimensional chains . . . . . . . . . . . . . . . . . . . . . . . 25 5.3 (Relatively) aspherical groups . . . . . . . . . . . . . . . . . . . . 30 5.4 The R. Thompson group . . . . . . . . . . . . . . . . . . . . . . . 32 5.5 E-trivial groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 ...

Duality for Groups

If F is known to be free, with generators gi, /3 may be constructed by setting j3g; = &», with bi so chosen that pbi = agi. Conversely, let F have the cited property and represent F as a quotient group Fo/Ro> where F0 is a free abelian group. Choose A—F and B = Fo in (1.1), let a be the identity, and p the given homomorphism of .Fo onto F with kernel Ro. Then, by (1.2), a=p/3 is an isomorphism,...

Duality for Sin-groups

The well-known duality theorem of Pontryagin and van Kampen [27, 20] states that the characters of an Abelian locally compact group G also form a group Ĝ, and the group of characters of Ĝ is isomorphic to G. For non-Abelian groups, there is no such duality. In a few words, difficulties on this way arise from the fact that the dual space of a noncommutative group, however defined, has no natural...

Coarse Alexander Duality and Duality Groups

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 G y X determines a collection of “peripheral” subgroups H1, . . . , Hk ⊂ G so that the...

Constructing Invariants for Finite Groups