New York Journal of Mathematics
Volume 18 (2012) 75-77

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Nathan M. Dunfield, Stavros Garoufalidis, Alexander Shumakovitch, and Morwen Thistlethwaite

Erratum: Behavior of knot invariants under genus 2 mutation

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Published: February 20, 2012
Keywords: mutation, symmetric surfaces, Khovanov Homology, volume, colored Jones polynomial, HOMFLY-PT polynomial, Kauffman polynomial, signature.
Subject: Primary 57N10, Secondary 57M25
Abstract
Proposition 2.7 of the original paper (Dunfield, Garoufalidis, Shumakovitch and Thistlethwaite, 2010) is false and as a result Corollary 2.8 has not been established. Here, we provide alternate proofs of the results in our paper which depended on those claims, with the exception of the invariance of generalized knot signatures. In particular, all the results claimed in Table 1.2 of the original paper have still been proved.
Acknowledgements

N. D. was partially supported by the supported by the Sloan Foundation. N. D. and S. G. were partially supported by the US NSF
Author information

Nathan M. Dunfield:
Dept. of Mathematics, MC-382, University of Illinois, Urbana, IL 61801, USA
nathan@dunfield.info

Stavros Garoufalidis:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA
stavros@math.gatech.edu

Alexander Shumakovitch:
George Washington University, Department of Mathematics, 1922 F Street, NW, Washington, DC 20052, USA
shurik@gwu.edu

Morwen Thistlethwaite:
Department of Mathematics, The University of Tennessee, Knoxville, TN 37996-1300, USA
morwen@math.utk.edu