English

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.

Keywords

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

R2 v1 2026-06-23T07:04:14.310Z