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Mutations of links in genus 2 handlebodies |
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| Authors: | D Cooper W B R Lickorish |
| Institution: | Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106 ; Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, United Kingdom |
| 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. |
| Keywords: | Alexander polynomial knot signature knot mutation Jones polynomial Melvin-Morton conjecture |
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