A homological approach to pseudoisotopy theory. I
Authors
Publication Date
2022-03Journal Title
no.
ISSN
0020-9910
Publisher
Springer Science and Business Media LLC
Volume
227
Issue
3
Pages
1093-1167
Language
en
Type
Article
This Version
VoR
Metadata
Show full item recordCitation
Krannich, M. (2022). A homological approach to pseudoisotopy theory. I. no., 227 (3), 1093-1167. https://doi.org/10.1007/s00222-021-01077-7
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 $\mathrm{BDiff}_\partial(D^{2n+1})$ in degrees up
to $2n-5$.
Keywords
Article, 57R52, 19D50, 57R65, 55P47
Sponsorship
European Research Council (756444)
Leverhulme Trust (PLP-2017-017)
Identifiers
s00222-021-01077-7, 1077
External DOI: https://doi.org/10.1007/s00222-021-01077-7
This record's URL: https://www.repository.cam.ac.uk/handle/1810/334326
Rights
Licence:
http://creativecommons.org/licenses/by/4.0/
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