Geodesic
Fibrewise rational H-spaces
Lupton, Gregory1 ; Smith, Samuel Bruce2
1Department of Mathematics, Cleveland State University, 2121 Euclid Avenue, Cleveland OH 44115, USA
2Department of Mathematics, Saint Joseph’s University, 5600 City Avenue, Philadelphia PA 19131, USA
Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1667-1694
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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.

DOI : 10.2140/agt.2012.12.1667
Classification : 55P62, 55P45, 55R70
Keywords: fiberwise homotopy, H-space, Hopf Theorem, Leray–Samelson Theorem, adjoint bundle, gauge group, Sullivan minimal model

Lupton, Gregory  1   ; Smith, Samuel Bruce  2

1 Department of Mathematics, Cleveland State University, 2121 Euclid Avenue, Cleveland OH 44115, USA
2 Department of Mathematics, Saint Joseph’s University, 5600 City Avenue, Philadelphia PA 19131, USA 
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Lupton, Gregory; Smith, Samuel Bruce. Fibrewise rational H-spaces. Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1667-1694. doi: 10.2140/agt.2012.12.1667

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