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Fibrewise rational
H-spaces
Gregory Lupton and Samuel Bruce Smith |
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Algebraic & Geometric Topology 12 (2012) 1667–1694
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 55P62
Secondary: 55P45, 55R70
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References |
Publication
Received: 9 January 2012
Revised: 24 April 2012
Accepted: 5 June 2012
Published: 4 August 2012
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Authors |
| Gregory Lupton | |
| Department of Mathematics Cleveland State University 2121 Euclid Avenue Cleveland OH 44115 USA |
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| 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 |
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| http://people.sju.edu/~smith | |
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