Finiteness conditions for graph-wreath products.

Peter Kropholler (University of Southampton)

Wednesday 22nd October, 2014 15:30-16:30 Maths 416

Abstract

The graph-wreath product of groups combines the idea of wreath product with that of graph product in a natural way. Given a simple graph and a group A one can construct a group B using copies of A at the vertices of the graph, commuting when two vertices are joined. If H is a group acting on the graph then the semidirect product of B and H is a natural group to consider.

Homological finiteness conditions for this group can be established from an understanding of those of A and H together with an understanding of cliques in the graph.  The methods use infinite Davis complexes and applications include some interesting examples of amenable groups based on Houghton’s groups. Thompson’s groups also provide examples for which the construction produces groups with strong finiteness conditions.

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