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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Splitting isomorphisms of mapping tori

Author: Terry C. Lawson
Journal: Trans. Amer. Math. Soc. 205 (1975), 285-294
MSC: Primary 57D80
MathSciNet review: 0358821
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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 $ {M_f} \to {N_g}$ is pseudoisotopic to an isomorphism which sends $ M$ to $ N$. An exact sequence for the group of pseudoisotopy classes of automorphisms of $ M \times {S^1}$ 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 of higher dimension where the $ s$-cobordism theorem is applied.

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Keywords: Homeomorphism, PL homeomorphism, diffeomorphism, invertible cobordism, pseudoisotopy, mapping torus, $ h$-cobordism, $ s$-cobordism theorem
Article copyright: © Copyright 1975 American Mathematical Society