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A homological approach to pseudoisotopy theory. I

Published version
Peer-reviewed

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Abstract

We construct a zig-zag from the once delooped space of pseudoisotopies of a closed 2n-disc to the once looped algebraic K-theory space of the integers and show that the maps involved are p-locally (2n−4)-connected for n>3 and large primes p. The proof uses the computation of the stable homology of the moduli space of high-dimensional handlebodies due to Botvinnik--Perlmutter and is independent of the classical approach to pseudoisotopy theory based on Igusa's stability theorem and work of Waldhausen. Combined with a result of Randal-Williams, one consequence of this identification is a calculation of the rational homotopy groups of BDiff(D2n+1) in degrees up to 2n−5.

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Keywords

math.AT, math.AT, math.GT, 57R52, 19D50, 57R65, 55P47

Journal Title

no.

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Journal ISSN

0020-9910
1432-1297

Volume Title

227

Publisher

Springer Science and Business Media LLC
Sponsorship
European Research Council (756444)
Leverhulme Trust (PLP-2017-017)