Topological Lagrangians and cohomology
Abstract
Witten [12] has interpreted the Donaldson invariants of four-manifolds by means of a topological Lagrangian. We show that this Lagrangian should be understood in terms of an infinite-dimensional analogue of the Gauss-Bonnet formula. Starting with a formula of Mathai and Quillen for the Thom class, we obtain a formula for the Euler class of a vector bundle, which formally yields the explicit form of Witten's Lagrangian. We use the same method to treat Lagrangians proposed for the Casson invariant.
- Publication:
-
Journal of Geometry and Physics
- Pub Date:
- 1990
- DOI:
- 10.1016/0393-0440(90)90023-V
- Bibcode:
- 1990JGP.....7..119A