A homological approach to pseudoisotopy theory. I

• 成果类型: Article
• 署名作者: Krannich, Manuel
• 署名单位: University of Cambridge
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01077-7
• 发表日期: 2022
• 页码: 1093-1167
• 关键词: homotopy; bundles

摘要

We construct a zig-zag from the once delooped space of pseudoiso-topies 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(partial derivative) (D2n+1) in degrees up to 2n - 5.