SL-oriented cohomology theories
Abstract
We show that a representable motivic cohomology theory admits a unique normalized SLc-orientation if the zeroth cohomology presheaf is a Zariski sheaf. We also construct Thom isomorphisms in SL-oriented cohomology for SLc-bundles and obtain new results on the η-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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