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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Instanton homology and the Alexander polynomial

Author(s): Yuhan Lim
Journal: Proc. Amer. Math. Soc. 138 (2010), 3759-3768.
MSC (2010): Primary 57R58, 57M27
Posted: May 19, 2010
MathSciNet review: 2661575
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Abstract | References | Similar articles | Additional information

Abstract: We prove that the instanton knot homology $ KHI(K)$ as defined by Kronheimer-Mrowka recovers the Alexander polynomial for knots $ K$ in the 3-sphere.


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M. Culler, C. McA. Gordon, J. Luecke, P.B. Shalen, Dehn surgery on knots, Ann. of Math. (2), 125 (1987) No. 2, 237-300. MR 881270 (88a:57026)

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S.K. Donaldson, Floer homology groups in Yang-Mills theory, Cambridge Univ. Press, 2002. MR 1883043 (2002k:57078)

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K. Frøyshov, Equivariant aspects of Yang-Mills Floer theory, Topology, 41 (2002) No. 3, 525-552. MR 1910040 (2003b:57048)

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R. Fintushel, R.J. Stern, Knots, links and $ 4$-manifolds, Invent. Math., 134 (1998) No. 2, 363-400. MR 1650308 (99j:57033)

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P.B. Kronheimer, T.S. Mrowka, Knots, sutures and excision, preprint (2008).

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P.B. Kronheimer, T.S. Mrowka, Instanton Floer homology and the Alexander polynomial, preprint (2009).

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Additional Information:

Yuhan Lim
Affiliation: Murphys, California 95247
Email: ylim583@yahoo.com

DOI: 10.1090/S0002-9939-2010-10412-4
PII: S 0002-9939(2010)10412-4
Received by editor(s): July 28, 2009
Received by editor(s) in revised form: July 30, 2009 and January 26, 2010
Posted: May 19, 2010
Communicated by: Daniel Ruberman
Copyright of article: Copyright 2010, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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