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2009 Umkehr maps
Ralph L. Cohen, John R. Klein
Homology Homotopy Appl. 11(1): 17-33 (2009).

Abstract

In this note, we study umkehr maps in generalized (co)homology theories arising from the Pontrjagin-Thom construction, from integrating along fibers, pushforward homomorphisms, and other similar constructions. We consider the basic properties of these constructions and develop axioms which any umkehr homomorphism must satisfy. We use a version of Brown representability to show that these axioms completely characterize these homomorphisms, and a resulting uniqueness theorem follows. Finally, motivated by constructions in string topology, we extend this axiomatic treatment of umkehr homomorphisms to a fiberwise setting.

Citation

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Ralph L. Cohen. John R. Klein. "Umkehr maps." Homology Homotopy Appl. 11 (1) 17 - 33, 2009.

Information

Published: 2009
First available in Project Euclid: 1 September 2009

zbMATH: 1160.55005
MathSciNet: MR2475820

Subjects:
Primary: 55N99
Secondary: 55M05, 55R70

Rights: Copyright © 2009 International Press of Boston

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Vol.11 • No. 1 • 2009
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