Vol. 68, No. 2, 1977

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Gauge groups and classification of bundles with simple structural group

Wendell Dan Curtis and Forrest Miller

Vol. 68 (1977), No. 2, 331–338

Suppose πi i = 1,2 are principal K-bundles which are Cr-isomorphic in the sense that there exists a K-equivariant Cr-diffeomorphism f : 𝒫1 →𝒫2. If h belongs to the gauge group H2 of 𝒫2 then hf 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 Cr(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
Received: 8 June 1976
Published: 1 February 1977
Wendell Dan Curtis
Forrest Miller