Seminar on A1-topology, motives and K-theory

Motivic second Hopf map as an obstruction to symplectic orientation (1/2)

by Alexey Ananyevskiy (PDMI RAS)

Europe/Moscow
958-115-833 (Zoom)

958-115-833

Zoom

Description

I will give the construction of the motivic second Hopf map $\nu$ 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 $\mathbb{A}^1$-derived category does not admit Thom isomorphisms for oriented (and for symplectic) bundles.