Relative semicharacteristic classes

Abstract

In 1973 Ronnie Lee introduced the notion of semicharacteristic classes, which are invariants of the bordism group ℜ*(Bπ) of closed manifolds equipped with a free action of a finite group π. In this paper we relativize his theory. Associated to a homomorphism G → π of finite groups, there is the relative bordism group ℜ*(BG → Bπ), which is the bordism group of compact manifolds M with a free π-action, so that the action on ∂M is induced from a free G-action, i.e. ∂M = π xGN for some manifold N with a free G-action. The invariants defined here are invariants of this relative group.