Sigma theory for Bredon modules

We develop new invariants similar to the Bieri-Strebel-Neumann-Renz invariants but in the category of Bredon modules (with respect to the class of the finite subgroups of G). We prove that for virtually soluble groups of type FP_{\infty} and finite extension of the Thompson group F the new invariants coincide with the classical ones

Subgroup posets, Bredon cohomology and equivariant Euler characteristics

For a discrete group $\Gamma$ satisfying some finiteness conditions we give a Bredon projective resolution of the trivial module in terms of projective covers of the chain complex associated to certain posets of subgroups. We use this to give new results on dimensions of $E\gamma$ and to reprove that for virtually solvable groups, \underline{\cd}\Gamma=\vcd\Gamma. We also deduce a formula to compute the Euler class of $E\gamma$ for $\Gamma$ virtually solvable of type \FP_\infty and use it to compute orbifold Euler characteristics.Comment: 19 page