Homological finiteness conditions for groups and monoids
Abstract: For both groups and monoids, homology is defined in terms of resolutions of projective modules over the integral group (or monoid) ring. For groups, this can also be defined topologically, in terms of K(G,1)-spaces, but for monoids there is no such correspondence. Squier has introduced a new topological space which captures homology in low dimensions, and which applies to both monoids and groups. In this talk I will discuss higher dimensional analogs of Squier's complexes.