Bordism groups of Poincare -coalgebras and symmetric -groups

Abstract

A Poincare -coalgebra construction over involutive algebras is introduced in this paper. Various types of bordism between Poincare -coalgebras are defined and the relations between the corresponding bordism groups are studied. It is shown in particular that the Thom bordism groups of closed non-oriented smooth manifolds and the rational Wall groups of a unitary group have a common algebraic origin, that is, they are obtained by the same construction considered over the fields and , respectively.