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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.

Copyright 1999 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 05 (1999), pp. 146-156
• Publisher Identifier: S 1079-6762(99)00073-6
• 1991 Mathematics Subject Classification. Primary 57M25, 57Q45; Secondary 55N99, 18G99
• Key words and phrases. Knots, knotted surfaces, quandle cohomology, state-sum invariants
• Received by the editors May 28, 1999
• Posted on December 9, 1999
• Communicated by Walter Neumann
• Comments (When Available)

J. Scott Carter

Department of Mathematics, University of South Alabama, Mobile, AL 36688

E-mail address: carter@mathstat.usouthal.edu

Daniel Jelsovsky

Department of Mathematics, University of South Florida, Tampa, FL 33620

E-mail address: jelsovsk@math.usf.edu

Seiichi Kamada

Department of Mathematics, Osaka City University, Osaka 558-8585, JAPAN

Current address: Department of Mathematics, University of South Alabama, Mobile, AL 36688

E-mail address: kamada@sci.osaka-cu.ac.jp, skamada@mathstat.usouthal.edu

Laurel Langford

Department of Mathematics, University of Wisconsin at River Falls, River Falls, WI 54022

E-mail address: laurel.langford@uwrf.edu

Masahico Saito

Department of Mathematics, University of South Florida, Tampa, FL 33620

E-mail address: saito@math.usf.edu

The third author was supported by a Fellowship from the Japan Society for the Promotion of Science.