Work

On the non-orientable 4-genus of torus knots with braid index 5 or 6

Year: 2025

Type: article

Abstract: The non-orientable 4-genus of a knot K in [Formula: see text], denoted [Formula: see text], measures the minimum genus of a non-orientable surface in [Formula: see text] bounded by K. We compute bounds for the non-orientable 4-genus of knots [Formula: see text] and [Formula: see text], extending previous research. Additionally, we provide a generalized, non-recursive formula for [Formula: see text], the d-invariant of-1-surgery on torus knots.

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s021821652650001x

Authors: Megan Fairchild, Hailey J. Garcia, Jake Murphy, Hannah Percle

Institution: Louisiana State University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Interactions Between Contact Geometry, Floer Theory and Low-Dimensional Topology, RTG: Topology, Representation Theory, and Mathematical Physics at Louisiana State University