Whitehead Doubles and Non-Orientable Surfaces

2024/10/17 by Fairchild, Megan
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2410.13736

Abstract

Whitehead doubles provide a plethora of examples of knots that are topologically slice but not smoothly slice. We discuss the problem of the Whitehead double of the Figure 8 knot and survey commonly used techniques to obstructing sliceness. Additionally, we improve bounds in general for the non-orientable 4 genus of t-twisted Whitehead doubles and provide genus 1 non-orientable cobordisms to cable knots.

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