Splitting isomorphisms of mapping tori

Abstract

Necessary and sufficient conditions involving invertible cobordisms are given for two mapping tori to be isomorphic. These are used to give conditions under which a given isomorphism Mf , Ng is pseudoisotopic to an isomorphism which sends M to N. An exact sequence for the group of pseudoisotopy classes of automorphisms of M X S1 is derived. The principal tools are an imbedding technique due to C. T. C. Wall as well as arguments involving invertible cobordisms. Applications and examples are given, particularly for manifolds or higher dimension where the s-cobordism theorem is applied.