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State-sum invariants of knotted curves and surfaces from quandle cohomology

Authors: J. Scott Carter, Daniel Jelsovsky, Seiichi Kamada, Laurel Langford and Masahico Saito
Journal: Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 146-156
MSC (1991): Primary 57M25, 57Q45; Secondary 55N99, 18G99
Published electronically: December 9, 1999
MathSciNet review: 1725613
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Abstract: State-sum invariants for classical knots and knotted surfaces in $4$-space are developed via the cohomology theory of quandles. Cohomology groups of quandles are computed to evaluate the invariants. Some twist spun torus knots are shown to be noninvertible using the invariants.

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Additional Information

J. Scott Carter
Affiliation: Department of Mathematics, University of South Alabama, Mobile, AL 36688

Daniel Jelsovsky
Affiliation: Department of Mathematics, University of South Florida, Tampa, FL 33620

Seiichi Kamada
Affiliation: Department of Mathematics, Osaka City University, Osaka 558-8585, JAPAN
Address at time of publication: Department of Mathematics, University of South Alabama, Mobile, AL 36688

Laurel Langford
Affiliation: Department of Mathematics, University of Wisconsin at River Falls, River Falls, WI 54022

Masahico Saito
Affiliation: Department of Mathematics, University of South Florida, Tampa, FL 33620

Keywords: Knots, knotted surfaces, quandle cohomology, state-sum invariants
Received by editor(s): May 28, 1999
Published electronically: December 9, 1999
Additional Notes: The third author was supported by a Fellowship from the Japan Society for the Promotion of Science.
Communicated by: Walter Neumann
Article copyright: © Copyright 1999 American Mathematical Society

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