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2010 Instanton Floer homology and the Alexander polynomial
Peter Kronheimer, Tomasz Mrowka
Algebr. Geom. Topol. 10(3): 1715-1738 (2010). DOI: 10.2140/agt.2010.10.1715

Abstract

The instanton Floer homology of a knot in the three-sphere is a vector space with a canonical mod 2 grading. It carries a distinguished endomorphism of even degree, arising from the 2–dimensional homology class represented by a Seifert surface. The Floer homology decomposes as a direct sum of the generalized eigenspaces of this endomorphism. We show that the Euler characteristics of these generalized eigenspaces are the coefficients of the Alexander polynomial of the knot. Among other applications, we deduce that instanton homology detects fibered knots.

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Peter Kronheimer. Tomasz Mrowka. "Instanton Floer homology and the Alexander polynomial." Algebr. Geom. Topol. 10 (3) 1715 - 1738, 2010. https://doi.org/10.2140/agt.2010.10.1715

Information

Received: 27 July 2009; Revised: 2 June 2010; Accepted: 13 June 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1206.57038
MathSciNet: MR2683750
Digital Object Identifier: 10.2140/agt.2010.10.1715

Subjects:
Primary: 57R58
Secondary: 57M25

Rights: Copyright © 2010 Mathematical Sciences Publishers

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Vol.10 • No. 3 • 2010
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