Bordism of algebras over Hopf algebras (Q1092448)

This article sets an algebraic analogue of topological bordism at the level of characteristic numbers. Given an algebra H over a graded Hopf algebra A, the author defines the nth A bordism group of H, \(\Omega_ n(A,H)\), for each \(n>0\). In the topological case A is the Steenrod algebra and H is the \({\mathbb{Z}}/(2)\)-cohomology of the space. \(\Omega_ n\) is a contravariant functor from the category of pairs (A,H), where H is an algebra over the Hopf algebra A, to the category of abelian groups. Finally, calculations of \(\Omega_ 1\) and \(\Omega_ 2\) are given.