Local formulae in equivariant bordisms
It is well known that if one localizes an equivariant bordism group \(\Omega^ G_ *(X)\) at certain primes dividing the order of \(G\), the result is a direct sum of ordinary bordism groups for the fixed sets of subgroups and appropriate normal bundles. In earlier work, the author established a formalism for this decomposition in terms of characteristic classes in cobordism theory. This paper is devoted to establishing the universal local formula for the fixed set of \(G\) itself. The main result is a formula for the equivariant Witt invariant, analogous to the Atiyah-Singer \(G\)-signature theorem.
scientific article; zbMATH DE number 167779