Analytic and topological invariants associated to nowhere zero vector fields

Weiping Zhang

Vol. 187 (1999), No. 2, 379–398

DOI: 10.2140/pjm.1999.187.379

Abstract

We construct skew-adjoint operators associated to nowhere zero vector fields on manifolds with vanishing Euler number. The mod 2 indices of these operators provide potentially new invariants for such manifolds. An odd index theorem for corresponding Toeplitz operators is established. This last result may be viewed as an odd dimensional analogue of the Gauss-Bonnet-Chern theorem.

Milestones

Received: 25 August 1997

Published: 1 February 1999