Volume 12, issue 3 (2012)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Fibrewise rational H-spaces

Gregory Lupton and Samuel Bruce Smith

Algebraic & Geometric Topology 12 (2012) 1667–1694
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 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.

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