Gauge theory and Rasmussen's invariant
Name
Mrowka_Gauge theory.pdf
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333.87 KB
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Checksum (MD5)
c3c04be1454699a9f8dcbcc4e6f4278c
Author(s)
Kronheimer, P. B.
Mrowka, Tomasz S.
Date Issued
April 2013
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1112/jtopol/jtt008
