State-sum invariants of knotted curves and surfaces from quandle cohomology. (English) Zbl 0995.57004
Summary: 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.
MSC:
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |
| 57Q45 | Knots and links in high dimensions (PL-topology) (MSC2010) |
| 55N99 | Homology and cohomology theories in algebraic topology |
| 18G99 | Homological algebra in category theory, derived categories and functors |
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
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