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Mutations of links in genus 2 handlebodies
Author(s):
D.
Cooper;
W.
B. R.
Lickorish
Journal:
Proc. Amer. Math. Soc.
127
(1999),
309-314.
MSC (1991):
Primary 57M25;
Secondary 81T99, 81R50
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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.
References:
- 1.
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- 2.
- J.Dean, Many classical knot invariants are not Vassiliev invariants, J. Knot Theory and its Ramifications 3 (1994), 7-10. MR 94k:57008
- 3.
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 ) invariant, J. Knot Theory and its Ramifications 3 (1994), 25-39. MR 95a:57025 - 4.
- P.M.Melvin and H.R.Morton, The coloured Jones function, Comm. Math. Phys. 169 (1995), 501-520. MR 96g:57012
- 5.
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- 6.
- K.Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965), 387-422. MR 30:1506
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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:
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
Copyright of article:
Copyright
1999,
American Mathematical Society
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