A Refinement of the Spanning Surface Defect in $3$ and $4$ Dimensions

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Julia Knihs, Jeanette Patel, Joshua M. Sabloff, Thea Rugg
DOI: 10.48550/arxiv.2602.13186
Cited by: 0

Abstract

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.

Fields of Study & Subjects

Geometric and Algebraic Topology Algebraic Geometry and Number Theory Advanced Graph Theory Research

Publication details

Journal / source
arXiv (Cornell University)
Publication date
13 February 2026
Language
EN
Document type
Preprint