Whitehead Doubles and Non-Orientable Surfaces
Geometric Topology
2024-10-29 v2
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 -twisted Whitehead doubles and provide genus 1 non-orientable cobordisms to cable knots.
Keywords
Cite
@article{arxiv.2410.13736,
title = {Whitehead Doubles and Non-Orientable Surfaces},
author = {Megan Fairchild},
journal= {arXiv preprint arXiv:2410.13736},
year = {2024}
}