Twist spinning of knots and metabolizers of Blanchfield pairings

2013/12/06 by Friedl, Stefan, Orson, Patrick
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1312.1934

Abstract

In a classic paper Zeeman introduced the k-twist spin of a knot K and showed that the exterior of a twist spin fibers over S¹. In particular this result shows that the knot K # -K is doubly slice. In this paper we give a quick proof of Zeeman's result. The k-twist spin of K also gives rise to two metabolizers for K # -K and we determine these two metabolizers precisely.

Related

• Twist spun knots of twist spun knots of classical knots
• Twist Spinning Knotted Trivalent Graphs
• Branched twist spins and knot determinants
• Gluck twists along 2-knots with periodic monodromy
• Irreducible SL(2,ℂ)-metabelian representations of branched twist spins