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The
surgery exact sequence, K-theory and the signature
operator
Paolo Piazza and Thomas Schick |
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Vol. 1 (2016), No. 2, 109–154
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Abstract |
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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. |
Keywords
signature operator, K-theory, exact surgery sequence, index
classes, rho-classes
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Mathematical Subject Classification 2010
Primary: 46L80, 46L87, 58J22
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Milestones
Received: 9 January 2015
Accepted: 7 April 2015
Published: 20 October 2015
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Authors |
| Paolo Piazza | |
| Dipartimento di Matematica Università degli Studi di Roma "La Sapienza" P.le Aldo Moro 5 I-00185 Roma Italy |
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| Thomas Schick | |
| Mathematisches Institut Georg-August-Universität Göttingen Bunsenstr. 3 D-37073 Göttingen Germany |
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