Fibrewise rational H-spaces. (English) Zbl 1248.55004
Authors’ abstract: We prove fibrewise versions of classical theorems of Hopf and Leray-Samelson. Our results imply the fibrewise H-triviality after rationalization of a certain class of fibrewise H-spaces. They apply, in particular, to universal adjoint bundles. From this, we may retrieve a result of M. C. Crabb and W. A. Sutherland [Proc. Lond. Math. Soc., III. Ser. 81, No. 3, 747–768 (2000; Zbl 1024.55005)], which is used there as a crucial step in establishing their main finiteness result.
Reviewer: Jean Claude Thomas (Angers)
Keywords:
fiberwise homotopy; H-space; Hopf theorem; Leray-Samelson theorem; adjoint bundle; gauge group; Sullivan minimal modelCitations:
Zbl 1024.55005References:
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