SL-oriented cohomology theories
Algebraic Geometry
2019-05-15 v2 Algebraic Topology
K-Theory and Homology
Abstract
We show that a representable motivic cohomology theory admits a unique normalized SL^c-orientation if the zeroth cohomology presheaf is a Zariski sheaf. We also construct Thom isomorphisms in SL-oriented cohomology for SL^c-bundles and obtain new results on the \eta-torsion characteristic classes, in particular, we prove that the Euler class of an oriented bundle admitting a (possibly non-orientable) odd rank subbundle is annihilated by the Hopf element.
Cite
@article{arxiv.1901.01597,
title = {SL-oriented cohomology theories},
author = {Alexey Ananyevskiy},
journal= {arXiv preprint arXiv:1901.01597},
year = {2019}
}
Comments
18 pages; v.2 minor updates