Gauge groups and classification of bundles with simple structural group

Wendell Dan Curtis and Forrest Miller

Vol. 68 (1977), No. 2, 331–338

DOI: 10.2140/pjm.1977.68.331

Abstract

Suppose π_i i = 1,2 are principal K-bundles which are C^r-isomorphic in the sense that there exists a K-equivariant C^r-diffeomorphism f : 𝒫₁ →𝒫₂. If h belongs to the gauge group H₂ of 𝒫₂ then h∘f lies in H₁ and we have a group isomorphism H₂ → H₁ which is C^∞. It is the purpose of this paper to investigate the converse in the case where K is a simple Lie group. (If K is abelian the gauge group of every K bundle over X is C^r(X,K) so there is no hope of a converse. However for simple groups the situation is much better).

Mathematical Subject Classification 2000

Primary: 55F15, 55F15

Secondary: 58D99

Milestones

Received: 8 June 1976

Published: 1 February 1977