Geodesic
Umkehr maps
Homology, homotopy, and applications, Tome 11 (2009) no. 1, pp. 17-33.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2009.v11.n1.a2
Classification : 55Nxx, 55M05, 55R70
Keywords: umkehr map, fibered spectrum, Poincaré duality, string topology 
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Ralph L. Cohen; John R. Klein. Umkehr maps. Homology, homotopy, and applications, Tome 11 (2009) no. 1, pp. 17-33. doi : 10.4310/HHA.2009.v11.n1.a2. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2009.v11.n1.a2/

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