Research ArticlesNo Access

Distinguishing mutant pretzel knots in concordance

Allison N. Miller

Department of Mathematics, University of Texas at Austin, Austin, TX 78712, USA

https://doi.org/10.1142/S0218216517500419Cited by:4 (Source: Crossref)

Abstract

We prove that many four-strand pretzel knots of the form $K = P (2 n, m, - 2 n \pm 1, - m)$ are not topologically slice, even though their positive mutants $P (2 n, - 2 n \pm 1, m, - m)$ are ribbon. We use the sliceness obstruction of Kirk and Livingston [Twisted Alexander invariants, Reidemeister torsion, and Casson–Gordon invariants, Topology38 (1999) 635–661], related to the twisted Alexander polynomials associated to prime power cyclic covers of knots.

Keywords:

AMSC: 57M25, 57M27

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