Constructing knots with low rational genera

Fuente: arXiv
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Autores principales: McDonald, Clayton, Miller, Allison N.
Formato: Preprint
Publicado: 2025
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author McDonald, Clayton
Miller, Allison N.
author_facet McDonald, Clayton
Miller, Allison N.
contents We give a flexible construction for knots in the 3-sphere that bound surfaces of unexpectedly low genus in punctured open books on 3-manifolds. We use this construction to give the first examples of knots whose genus differs in different $\mathbb{Z}/2\mathbb{Z}$ homology balls. We also establish that every knot bounds a M{ö}bius band in a rational homology ball, and that there are knots whose genus in $T^4$ and $B^4$ differ arbitrarily.
format Preprint
id arxiv_https___arxiv_org_abs_2511_15900
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Constructing knots with low rational genera
McDonald, Clayton
Miller, Allison N.
Geometric Topology
57K10
We give a flexible construction for knots in the 3-sphere that bound surfaces of unexpectedly low genus in punctured open books on 3-manifolds. We use this construction to give the first examples of knots whose genus differs in different $\mathbb{Z}/2\mathbb{Z}$ homology balls. We also establish that every knot bounds a M{ö}bius band in a rational homology ball, and that there are knots whose genus in $T^4$ and $B^4$ differ arbitrarily.
title Constructing knots with low rational genera
topic Geometric Topology
57K10
url https://arxiv.org/abs/2511.15900