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2002 Twisted quandle homology theory and cocycle knot invariants
J Scott Carter, Mohamed Elhamdadi, Masahico Saito
Algebr. Geom. Topol. 2(1): 95-135 (2002). DOI: 10.2140/agt.2002.2.95


The quandle homology theory is generalized to the case when the coefficient groups admit the structure of Alexander quandles, by including an action of the infinite cyclic group in the boundary operator. Theories of Alexander extensions of quandles in relation to low dimensional cocycles are developed in parallel to group extension theories for group cocycles. Explicit formulas for cocycles corresponding to extensions are given, and used to prove non-triviality of cohomology groups for some quandles. The corresponding generalization of the quandle cocycle knot invariants is given, by using the Alexander numbering of regions in the definition of state-sums. The invariants are used to derive information on twisted cohomology groups.


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J Scott Carter. Mohamed Elhamdadi. Masahico Saito. "Twisted quandle homology theory and cocycle knot invariants." Algebr. Geom. Topol. 2 (1) 95 - 135, 2002.


Received: 27 September 2001; Accepted: 8 February 2002; Published: 2002
First available in Project Euclid: 21 December 2017

zbMATH: 0991.57005
MathSciNet: MR1885217
Digital Object Identifier: 10.2140/agt.2002.2.95

Primary: 57N27, 57N99
Secondary: 57M25, 57Q45, 57T99

Rights: Copyright © 2002 Mathematical Sciences Publishers


Vol.2 • No. 1 • 2002
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