2020/02/29 by Manuel Krannich · 3 citations
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic number #Algebraic structures and combinatorial models #Computer science #Discrete mathematics #Homology (biology) #Homotopy #Homotopy and Cohomology in Algebraic Topology #Homotopy group #Mathematical analysis #Mathematics #Moduli space #Pure mathematics #Space (punctuation) #math.AT #math.GT #msc:19D50 #msc:55P47 #msc:57R52 #msc:57R65 #n-connected
paper · pdf · open access · doi:10.1007/s00222-021-01077-7
published in Inventiones mathematicae 227(3), 1093-1167 (Springer Science+Business Media) · 46 pages, to appear in Inventiones Mathematicae
arxiv created 2021/09/23 · openalex publication_date 2022/01/31 · arxiv updated 2022/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.