Electronic Research Announcements

Author(s): J. Scott Carter; Daniel Jelsovsky; Seiichi Kamada; Laurel Langford; Masahico Saito
Journal: Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 146-156.
MSC (1991): Primary 57M25, 57Q45; Secondary 55N99, 18G99
Posted: December 9, 1999
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Abstract: State-sum invariants for classical knots and knotted surfaces in

-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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Retrieve articles in Electronic Research Announcements with MSC (1991): 57M25, 57Q45, 55N99, 18G99

J. Scott Carter
Affiliation: Department of Mathematics, University of South Alabama, Mobile, AL 36688
Email: carter@mathstat.usouthal.edu

Daniel Jelsovsky
Affiliation: Department of Mathematics, University of South Florida, Tampa, FL 33620
Email: jelsovsk@math.usf.edu

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
Email: kamada@sci.osaka-cu.ac.jp, skamada@mathstat.usouthal.edu

Laurel Langford
Affiliation: Department of Mathematics, University of Wisconsin at River Falls, River Falls, WI 54022
Email: laurel.langford@uwrf.edu

Masahico Saito
Affiliation: Department of Mathematics, University of South Florida, Tampa, FL 33620
Email: saito@math.usf.edu

DOI: 10.1090/S1079-6762-99-00073-6
PII: S 1079-6762(99)00073-6
Keywords: Knots, knotted surfaces, quandle cohomology, state-sum invariants
Received by editor(s): May 28, 1999
Posted: 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
Copyright of article: Copyright 1999, American Mathematical Society

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