Year: 2024
Type: article
Abstract: Integrally oriented normally nonsingular maps between singular spaces have associated transfer homomorphisms on KO-homology at odd primes. We prove that such transfers preserve Siegel–Sullivan orientations, defined when the singular spaces are compact pseudomanifolds satisfying the Witt condition, for example pure-dimensional compact complex algebraic varieties. This holds for bundle transfers associated to block bundles with manifold fibers as well as for Gysin restrictions associated to normally nonsingular inclusions. Our method is based on constructing a lift of the Siegel–Sullivan orientation to a morphism of highly structured ring spectra which factors through L-theory.
Source: Journal of Topology and Analysis
Author: Markus Banagl
Institution: Heidelberg University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4402685101