Symplectic bordism: something old and something new

Speaker:

Andrew Baker

Affiliation:

University of Glasgow

Date:

Mon, 27/01/2020 - 15:00 - 16:00

Location:

MPIM Lecture Hall [2]

Parent event:

MPIM Topology Seminar [3]

I will begin by reviewing the history of the stable homotopy theory approach to understanding (co)bordism groups via the Pontrjagin-Thom isomorphism and analysis of the homotopy type of the associated Thom spectra. This proved remarkably successful and led to the determination of many important classical examples of bordism groups such as unoriented, oriented, unitary, special unitary, spin and spin^c. The two outstanding classical cases which are not completely understood are framed bordism (aka stable homotopy groups of spheres) and symplectic bordism. More recently attention has turned to String bordism and its variants.

I will review the basic ideas of symplectic bordism and explain some of the unusual issues that arise when studying it. In particular I will describe Ray's infinite family of elements of order 2 which appear to be `chromatic' in nature and play a crucial part in the work of Vershinen et al.

I will describe some recent work (partly joint with Nigel Ray) on orientations for quasi-symplectic bundles as introduced by Landweber in a paper ca 1965, and a corresponding bordism theory.