Fibrewise rational H-spaces

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 Crabb and Sutherland [Proc. London Math. Soc. 81 (2000) 747–768], which is used there as a crucial step in establishing their main finiteness result.

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Keywords

fiberwise homotopy, H-space, Hopf Theorem, Leray–Samelson Theorem, adjoint bundle, gauge group, Sullivan minimal model

Mathematical Subject Classification 2010

Primary: 55P62

Secondary: 55P45, 55R70

References

Publication

Received: 9 January 2012

Revised: 24 April 2012

Accepted: 5 June 2012

Published: 4 August 2012

Authors

Gregory Lupton
Department of Mathematics Cleveland State University 2121 Euclid Avenue Cleveland OH 44115 USA
http://facultyprofile.csuohio.edu/csufacultyprofile/detail.cfm?FacultyID=G_LUPTON
Samuel Bruce Smith
Department of Mathematics Saint Joseph’s University 5600 City Avenue Philadelphia PA 19131 USA
http://people.sju.edu/~smith

Volume 12, issue 3 (2012)

Gregory Lupton and Samuel Bruce Smith

Abstract