Geodesic
State-sum invariants of knotted curves and surfaces from quandle cohomology
Carter, J.1 ; Jelsovsky, Daniel2 ; Kamada, Seiichi3, 1 ; Langford, Laurel4 ; Saito, Masahico2
1 Department of Mathematics, University of South Alabama, Mobile, AL 36688
2 Department of Mathematics, University of South Florida, Tampa, FL 33620
3 Department of Mathematics, Osaka City University, Osaka 558-8585, JAPAN
4 Department of Mathematics, University of Wisconsin at River Falls, River Falls, WI 54022
Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 146-156 Cet article a éte moissonné depuis la source American Mathematical Society

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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.
DOI : 10.1090/S1079-6762-99-00073-6

Carter, J. 1 ; Jelsovsky, Daniel 2 ; Kamada, Seiichi 3, 1 ; Langford, Laurel 4 ; Saito, Masahico 2

1 Department of Mathematics, University of South Alabama, Mobile, AL 36688
2 Department of Mathematics, University of South Florida, Tampa, FL 33620
3 Department of Mathematics, Osaka City University, Osaka 558-8585, JAPAN
4 Department of Mathematics, University of Wisconsin at River Falls, River Falls, WI 54022 
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Carter, J.; Jelsovsky, Daniel; Kamada, Seiichi; Langford, Laurel; Saito, Masahico. State-sum invariants of knotted curves and surfaces from quandle cohomology. Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 146-156. doi: 10.1090/S1079-6762-99-00073-6

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