Infiniteness of A-types of gauge groups

Daisuke Kishimoto, Mitsunobu Tsutaya

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1 Citation (Scopus)

Abstract

Let G be a compact connected Lie group and let P be a principal G-bundle over K. The gauge group of P is the topological group of automorphisms of P. For fixed G and K, consider all principal G-bundles P over K. It is proved in Crabb and Sutherland [Proc. London Math. Soc. (3) 81 (2000) 747-768] and Tsutaya [J. London Math. Society 85 (2012) 142-164] that the number of An-types of the gauge groups of P is finite if n < ∞ and K is a finite complex. We show that the number of A-types of the gauge groups of P is infinite if K is a sphere and there are infinitely many P.

Original languageEnglish
Article numberjtv025
Pages (from-to)181-191
Number of pages11
JournalJournal of Topology
Volume9
Issue number1
DOIs
Publication statusPublished - Jul 29 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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