Geodesic
Bundle transfer of L–homology orientation classes for singular spaces
Banagl, Markus1
1 Institut für Mathematik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
Algebraic and Geometric Topology, Tome 24 (2024) no. 5, pp. 2579-2618

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We consider transfer maps on ordinary homology, bordism of singular spaces and homology with coefficients in Ranicki’s symmetric L–spectrum, associated to block bundles with closed oriented PL manifold fiber and compact polyhedral base. We prove that if the base polyhedron is a Witt space, for example a pure-dimensional compact complex algebraic variety, then the symmetric L–homology orientation of the base, constructed by Laures, McClure and the author, transfers to the L–homology orientation of the total space. We deduce from this that the Cheeger–Goresky–MacPherson L–class of the base transfers to the product of the L–class of the total space with the cohomological L–class of the stable vertical normal microbundle.

DOI : 10.2140/agt.2024.24.2579
Keywords: transfer homomorphisms, stratified spaces, intersection homology, characteristic classes, algebraic $L$–Theory, block bundles, cobordism

Banagl, Markus 1

1 Institut für Mathematik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 
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Banagl, Markus. Bundle transfer of L–homology orientation classes for singular spaces. Algebraic and Geometric Topology, Tome 24 (2024) no. 5, pp. 2579-2618. doi: 10.2140/agt.2024.24.2579

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