Alexey Ananyevskiy | Motivic second Hopf map as an obstruction to symplectic orientation(in Russian)
Channel: EIMI, PDMI RAS and Chebyshev Laboratory
Date: 2020-11-06

Seminar on A1-topology, motives and K-theory, October 01, 2020
Alexey Ananyevskiy (PDMI RAS)
Motivic second Hopf map as an obstruction to symplectic orientation (in Russian)

I will give the construction of the motivic second Hopf map ν in terms of framed correspondences and show that the nonvanishing of the corresponding element in generalized motivic cohomology gives an obstruction to the existence of symplectic Thom isomorphisms. As a corollary we will see that the stable A1-derived category does not admit Thom isomorphisms for oriented (and for symplectic) bundles.