Generalized spin structures and homogeneous spaces

Abstract: Spin geometry is a useful tool to describe geometric properties of manifolds. For instance, it is well-known that a manifold admitting parallel spinors has to be Ricci flat. Another example is Seiberg-Witten theory which relies on the existence of a notion of spin structure on 4-manifolds. However not every manifold admits a classical spin structure. In this talk we generalise this notion, so that every manifold admits a generalised spin structure. We look at obstructions for such structure and study their G-equivariance in the case of homogeneous spaces G/H. We will discuss the spheres as an example.

differential geometry

Audience: researchers in the topic

( video )

---

Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Differential geometry.

The seminar meets every other Wednesday. To accommodate most time zones, the time rotates. The Zoom link is sent to the mailing list around 24 hours before each talk. To subscribe to the mailing list, fill the following form: docs.google.com/forms/d/e/1FAIpQLSdKrJ-nivgjr7ZVJmIY0qkN-VbzTl5NHHNyg6nNsCqjhB-4WA/viewform?usp=sf_link.

---