Gluck twists along 2-knots with periodic monodromy

2018/11/13 by Fukuda, Mizuki
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1811.05109

Abstract

The union of singular orbits of an effective locally smooth circle action on the 4-sphere consists of two 2-knots, K and K^′, intersecting at two points transversely. Each of K and K^′ is called a branched twist spin. A twist spun knot is an example of a branched twist spin. The Gluck twists along branched twist spins are studied by Fintushel, Gordon and Pao. In this paper, we determine the 2-knot obtained from K by the Gluck twist along K^′. As an application, we give infinitely many pairs of inequivalent branched twist spins whose complements are homeomorphic.

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