1999
DOI: 10.1090/s1079-6762-99-00073-6
|View full text |Cite
|
Sign up to set email alerts
|

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

Abstract: Abstract. 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.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
23
0

Year Published

2001
2001
2020
2020

Publication Types

Select...
5
2

Relationship

0
7

Authors

Journals

citations
Cited by 42 publications
(23 citation statements)
references
References 26 publications
0
23
0
Order By: Relevance
“…Lemma 3.20 [Carter et al 1999;2003b]. The state-sum S λ Q is invariant under Reidemeister moves and thus defines a knot invariant S λ Q : → ‫ޚ‬ .…”
Section: Amentioning
confidence: 99%
See 2 more Smart Citations
“…Lemma 3.20 [Carter et al 1999;2003b]. The state-sum S λ Q is invariant under Reidemeister moves and thus defines a knot invariant S λ Q : → ‫ޚ‬ .…”
Section: Amentioning
confidence: 99%
“…Every quandle colouring number F q Q is the specialization of some knot colouring polynomial P x G . Quandle cohomology was initially studied in order to construct invariants in low-dimensional topology: in [Carter et al 1999;2003b] it was shown how a 2-cocycle λ ∈ Z 2 (Q, ) gives rise to a state-sum invariant of knots, S λ Q : → ‫ޚ‬ , which refines the quandle colouring number F Q . We prove the following result: Theorem 1.11 (Section 3E).…”
Section: Put Itmentioning
confidence: 99%
See 1 more Smart Citation
“…We have a 3-cocycle θ 5 ∈ Z (Z 5 , U (1)) satisfying the conditions (Coc1) and (Coc2) in Theorem 3•8, for example, as the following map. (2,2,4) • t 4 (2,4,2) • t (2,4,3) •t (3,1,2) • t 4 (3,1,3) • t (3,3,1) • t 4 (3,3,3) • t (3,4,2) • t 4…”
Section: •2 An Example Of Invariantsmentioning
confidence: 99%
“…Computing the state sum invariant I θ 5 with this 3-cocycle θ 5 for the lens spaces L(5, 1) and L (5,2), where their diagrams of labelled links are depicted in Figure 20 and 21 respectively, we have The Seifert manifold M = (S 2 ; 5, 5, . .…”
Section: •2 An Example Of Invariantsmentioning
confidence: 99%