Examples of Homologically Wide Actions

Abstract An action of a finite group G on manifold M is homologically wide if the first homology contains regular representation group. In this chapter, we study notion independently rest monograph. We case where surface and acts freely, using Lefschetz fixed point formula. then recall result Broughton that allows us to deal with general Riemann surface. After this, switch higher dimensional manifolds. Curtis’s theory virtual characters, use results Cooper Long construct examples counterexamples homological wideness in all dimensions ≥ 3. Finally, locally symmetric spaces. Property (T) implies only rank 1 interesting, make some remarks relation automorphic representations Mostow rigidity. an example torsion homology: Mednykh’s explicit computation Seifert-Weber dodecahedral space, which identify known modular through Brauer characters.