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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mutations of links in genus 2 handlebodies


Authors: D. Cooper and W. B. R. Lickorish
Journal: Proc. Amer. Math. Soc. 127 (1999), 309-314
MSC (1991): Primary 57M25; Secondary 81T99, 81R50
MathSciNet review: 1605940
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Abstract: A short proof is given to show that a link in the 3-sphere and any link related to it by genus 2 mutation have the same Alexander polynomial. This verifies a deduction from the solution to the Melvin-Morton conjecture. The proof here extends to show that the link signatures are likewise the same and that these results extend to links in a homology 3-sphere.


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Additional Information

D. Cooper
Affiliation: Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106
Email: cooper@math.ucsb.edu

W. B. R. Lickorish
Affiliation: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, United Kingdom
Email: wbrl@dpmms.cam.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04871-6
PII: S 0002-9939(99)04871-6
Keywords: Alexander polynomial, knot signature, knot mutation, Jones polynomial, Melvin-Morton conjecture
Received by editor(s): May 13, 1997
Additional Notes: This research was supported in part by N.S.F. grants DMS9504438 and DMS9510505.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1999 American Mathematical Society