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- Title
A homological approach to pseudoisotopy theory. I.
- Authors
Krannich, Manuel
- 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 (2 n - 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 ∂ (D 2 n + 1) in degrees up to 2 n - 5 .
- Subjects
HOMOTOPY groups; ALGEBRAIC spaces; K-theory; INTEGERS
- Publication
Inventiones Mathematicae, 2022, Vol 227, Issue 3, p1093
- ISSN
0020-9910
- Publication type
Article
- DOI
10.1007/s00222-021-01077-7