Distinguishing some genus one knots using finite quotients

2022/10/28 by Cheetham-West, Tamunonye
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2210.16426

Abstract

We give a criterion for distinguishing a prime knot K in S³ from every other knot in S³ using the finite quotients of π₁(S³∖ K). Using recent work of Baldwin-Sivek, we apply this criterion to the hyperbolic knots 5₂, 15n₄₃₅₂₂, and the three-strand pretzel knots P(-3,3,2n+1) for every integer n.

Related

• Determining knot groups by finite quotients
• Embedding infinite cyclic covers of knot spaces into 3-space
• Pretzel knots up to nine crossings
• Computing the unknotting numbers of certain pretzel knots
• Pretzel Knots with Unknotting Number One