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arXiv · 1901.01597

SL-oriented cohomology theories

Alexey Ananyevskiy
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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.

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Alexey Ananyevskiy. 2019-01-06. SL-oriented cohomology theories. https://arxiv.org/abs/1901.01597

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