Pants distances of knotted surfaces in 4-manifolds

Román Aranda; Sarah Blackwell; Devashi Gulati; Homayun Karimi; Geunyoung Kim; Nicholas Paul Meyer; Puttipong Pongtanapaisan

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arXiv · 2307.13874

Pants distances of knotted surfaces in 4-manifolds

Román Aranda·Sarah Blackwell·Devashi Gulati·Homayun Karimi·Geunyoung Kim·Nicholas Paul Meyer·Puttipong Pongtanapaisan

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Abstract

We define a pants distance for knotted surfaces in 4-manifolds, which generalizes the complexity studied by Blair-Campisi-Taylor-Tomova for surfaces in the 4-sphere. We determine that if the distance computed on a given diagram does not surpass a theoretical bound in terms of the multisection genus, then the pair (X, F) admits a standard form (i.e., has simple topology). Furthermore, we calculate the exact values of our invariants for many new examples, such as the spun lens spaces. We provide a characterization of genus two quadrisections with distance at most six.

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Román Aranda, Sarah Blackwell, Devashi Gulati, Homayun Karimi, Geunyoung Kim, Nicholas Paul Meyer, Puttipong Pongtanapaisan. 2023-07-26. Pants distances of knotted surfaces in 4-manifolds. https://arxiv.org/abs/2307.13874

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