Witten spinors on nonspin manifolds

Friday, September 27, 2013 -
4:15pm to 5:15pm
Unlike a 3-dimensional manifold, a higher dimensional manifold need not be spin. On an oriented Riemannian manifold the obstruction to having a spin structure is given by the second Stiefel-Whitney class. I will show that even when this obstruction does not vanish, it is still possible to define a notion of singular spin structure and associated singular Dirac operator. Then, modeling on Witten's proof of the Positive Mass Theorem, I will define the notion of Witten spinor on an asymptotically flat nonspin manifold, show their existence and describe their properties.
Speaker: 
Anda Degeratu
Albert-Ludwig Universitaet Feiburg
Event Location: 
Fine Hall 314