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Chern–Gauss–Bonnet and Lefschetz duality from a currential point of view.
- Source :
-
Advances in Mathematics . Sep2017, Vol. 317, p718-757. 40p. - Publication Year :
- 2017
-
Abstract
- We use the mapping cone for the relative deRham cohomology of a manifold with boundary in order to show that the Chern–Gauss–Bonnet Theorem for oriented Riemannian vector bundles over such manifolds is a manifestation of Lefschetz Duality in any of the two embodiments of the latter. We explain how Thom isomorphism fits into this picture, complementing thus the classical results about Thom forms with compact support. When the rank is odd , we construct, by using secondary transgression forms introduced here, a new closed pair of forms on the disk bundle associated to a vector bundle, pair which is Lefschetz dual to the zero section. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 317
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 124472723
- Full Text :
- https://doi.org/10.1016/j.aim.2017.07.005