On self H-equivalences of an H-space with respect to any multiplication
type: Item
instance of: scholarly article
title: On self H-equivalences of an H-space with respect to any multiplication
zbMATH Open document ID: 0602.55005
author: Norichika Sawashita
author: Masahiro Sugawara
published in: Hiroshima Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: An H-space usually supports many H-multiplications. The authors study the group HE(X) of self-homotopy equivalences which are H-maps for all possible multiplications. In particular it is shown that if X is U(n), SU(n) or Sp(n), then HE(X) is a finite nilpotent group and any member induces the identity on \(\pi_*(X)_{(p)}\) for all sufficiently large primes p. The proofs are not obvious and demonstrate considerable technical skill. Roughly speaking, the strategy is to replace the calculation of HE(X) by that of the group of H-equivalences for a particular multiplication and other groups depending only on the space without reference to H- structures, then to analyse the situation for a direct product of H- spaces and finally to localize at a sufficiently large prime so that X becomes a product of spheres and convenient multiplications can be chosen on each factor. The proof of nilpotency now depends upon earlier resuls quoted from the literature. In addition the paper includes other theorems and examples of interest.
reviewed by: J. R. Hubbuck
Mathematics Subject Classification ID: 55P45
Mathematics Subject Classification ID: 55P10
zbMATH DE Number: 3971759
zbMATH Keywords: H-space
zbMATH Keywords: H-multiplications
zbMATH Keywords: self-homotopy equivalences
zbMATH Keywords: H-maps
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3971759