Pure Maths Colloquium - Finiteness properties of totally disconnected locally compact groups - Ilaria Castellano (Southampton) Seminar

Event details

Recall that a totally disconnected locally compact (t.d.l.c.) group G is said to be of type FPₙ (resp. FP∞), if the trivial module ℚ admits a rational discrete projective resolution P* which is finitely generated in dimensions ≤ n (resp. in all dimensions). For example, G is of type FP₁ if and only if it is compactly generated. We give necessary and sufficient conditions for G to be of type FPₙ. Namely, both Bieri’s criterion and Brown’s criterion continue to hold in the context of t.d.l.c. groups. Finally, we show how Brown’s criterion can be then used to prove that property FPₙ is preserved by quasi-retractions, and in particular it is invariant under quasi-isometries. This is joint work-in-progress with G. Corob Cook.