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Bibliographic Details
Main Authors: Knihs, Julia, Patel, Jeanette, Sabloff, Joshua M., Rugg, Thea
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2602.13186
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author Knihs, Julia
Patel, Jeanette
Sabloff, Joshua M.
Rugg, Thea
author_facet Knihs, Julia
Patel, Jeanette
Sabloff, Joshua M.
Rugg, Thea
contents The spanning surface defect uses spanning surfaces of a knot in the $3$-sphere to measure how far a knot is from being alternating. We refine the spanning surface defect and extend the definition to take into account surfaces in the $4$-ball. We use these extensions to make comparisons between the $3$- and $4$-dimensional settings, to reframe non-orientable slice-torus bounds on the non-orientable $4$-genus, and to prove a connected sum formula.
format Preprint
id arxiv_https___arxiv_org_abs_2602_13186
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A Refinement of the Spanning Surface Defect in $3$ and $4$ Dimensions
Knihs, Julia
Patel, Jeanette
Sabloff, Joshua M.
Rugg, Thea
Geometric Topology
57K10
The spanning surface defect uses spanning surfaces of a knot in the $3$-sphere to measure how far a knot is from being alternating. We refine the spanning surface defect and extend the definition to take into account surfaces in the $4$-ball. We use these extensions to make comparisons between the $3$- and $4$-dimensional settings, to reframe non-orientable slice-torus bounds on the non-orientable $4$-genus, and to prove a connected sum formula.
title A Refinement of the Spanning Surface Defect in $3$ and $4$ Dimensions
topic Geometric Topology
57K10
url https://arxiv.org/abs/2602.13186