A Generalization of the Leray-Schauder Index Formula.
Abstract
This paper generalizes the Leray-Schauder index formula to the case where the inverse image of a point consists of a smooth manifold, assuming some nondegeneracy condition is satisfied on the manifold. The result states that the index is the Euler characteristic of a certain vector bundle over the manifold. Under slightly stronger nondegeneracy conditions, the index is in fact the Euler characteristics of the manifold. The paper also includes a discussion of the Euler characteristic for vector bundles and a simple proof of the Gauss-Bonnet-Chern theorem. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1981
- Accession Number
- ADA099363
Entities
People
- Jeremy Sylvester
Organizations
- University of Wisconsin–Madison