Instanton Floer homology and the Alexander polynomial
Name
Mrowka_Instanton Floer (arxiv).pdf
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416.12 KB
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Author(s)
Kronheimer, P. B.
Mrowka, Tomasz S.
Date Issued
August 2010
Journal
Algebraic & Geometric Topology
Publisher
Mathematical Sciences Publishers
Citation
Kronheimer, P. B., and T. S. Mrowka. “Instanton Floer Homology and the Alexander Polynomial.” Algebraic & Geometric Topology 10.3 (2010): 1715–1738. Web. 27 June 2012.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.2140/agt.2010.10.1715
