The 2-generalized knot group determines the knot

Abstract

Generalized knot groups $G_n(K)$ were introduced independently by Kelly (1991) and Wada (1992). We prove that $G_2(K)$ determines the unoriented knot type and sketch a proof of the same for $G_n(K)$ for $n>2$.

4 pages

References in corpus (1)

• Canonical decompositions of 3-manifolds

Cited by in corpus (4)

• Generalized quandle polynomials
• Generalised knot groups distinguish the square and granny knots (with an appendix by David Savitt)
• Link invariants derived from multiplexing of crossings
• Distinguishing the generalised knot groups of square and granny knot analogues