The G-bordism groups

Abstract

This chapter serves as a transition between the preceding purely topological chapters and the following chapters which deal specifically with periodic maps. In section 19 we interpret Ω _n (B(G)), G a finite group, as a group of bordism classes of pairs (G, M ⁿ) consisting of a closed oriented manifold M ⁿ and an orientation preserving differentiable free action of G on M ⁿ. Section 20 deals with a bordism analogue of the classical transfer homomorphism. Sections 21 and 22 give elementary properties of differentiable actions on a compact n-manifold B ⁿ, in particular an equivariant collaring theorem and a discussion of tubular neighborhoods of invariant submanifolds.