An absolute version of the Gromov-Lawson relative index theorem

Autor:	Hochs, Peter, Wang, Hang
Rok vydání:	2021
Předmět:	Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	A Dirac operator on a complete manifold is Fredholm if it is invertible outside a compact set. Assuming a compact group to act on all relevant structure, and the manifold to have a warped product structure outside such a compact set, we express the equivariant index of such a Dirac operator as an Atiyah-Segal-Singer type contribution from inside this compact set, and a contribution from outside this set. Consequences include equivariant versions of the relative index theorem of Gromov and Lawson, in the case of manifolds with warped product structures at infinity, and the Atiyah-Patodi-Singer index theorem. Comment: Added an assumption to the main result (a warped product structure outside a compact set) used to prove Lemma 3.4
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2110.00376 Zobrazit plný text záznamu View this record from Arxiv