The surgery exact sequence, K-theory and the signature operator

Autor:	Piazza, Paolo, Schick, Thomas
Rok vydání:	2013
Předmět:	Mathematics - K-Theory and Homology Mathematics - Differential Geometry Mathematics - Geometric Topology 19J25 19K99
Zdroj:	AKT 1 (2016) 109-154
Druh dokumentu:	Working Paper
DOI:	10.2140/akt.2016.1.109
Popis:	The main result of this paper is a new and direct proof of the natural transformation from the surgery exact sequence in topology to the analytic K-theory sequence of Higson and Roe. Our approach makes crucial use of analytic properties and new index theorems for the signature operator on Galois coverings with boundary. These are of independent interest and form the second main theme of the paper. The main technical novelty is the use of large scale index theory for Dirac type operators that are perturbed by lower order operators. Comment: 29 pages, AMS-LaTeX; v2: small corrections and (hopefully) improved exposition, as suggested by the referee. Final version, to appear in Annals of K-Theory
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1309.4370 Zobrazit plný text záznamu View this record from Arxiv