Gauge theory and Rasmussen's invariant

Author(s)
Kronheimer, P. B.; Mrowka, Tomasz S.
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Abstract
Using a version of instanton homology, an integer invariant s[superscript ♯](K) is defined for knots K in S[superscript 3]. This invariant is shown to be equal to Rasmussen's s-invariant. While Rasmussen's invariant provides a lower bound for 2 g(Σ) for any surface Σ in B[superscript 4] with boundary K, it is shown in this paper that s[superscript ♯](K) (and therefore s(K)) similarly bounds the genus of such a surface Σ in any homotopy 4-ball.
Date issued
2013-04
URI
http://hdl.handle.net/1721.1/93159
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Journal of Topology
Publisher
Oxford University Press - London Mathematical Society
Citation
Kronheimer, P. B., and T. S. Mrowka. “Gauge Theory and Rasmussen’s Invariant.” Journal of Topology 6.3 (April 7, 2013): 659–674.
Version: Original manuscript
ISSN
1753-8416
1753-8424
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