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

### J. Scott Carter, Daniel Jelsovsky, Seiichi Kamada, Laurel Langford and Masahico Saito

**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.

*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.

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