On slope genera of knotted tori in 4-space
Yi Liu, Yi Ni, Hongbin Sun, and Shicheng Wang
TL;DR
This paper explores the concept of slope genera for knotted tori in 4-space, comparing different definitions and examining their implications for the mapping class group's extendable subgroup.
Contribution
It introduces and compares various formulations of slope genera for knotted tori and applies these to study the extendable subgroup of their mapping class group.
Findings
Different formulations of slope genera are compared.
The notion is used to analyze the extendable subgroup.
Insights into the structure of the mapping class group are provided.
Abstract
In this note, we investigate genera for the slopes of a knotted torus in the 4-sphere analogous to the genus of a classical knot. We compare various formulations of this notion, and use this notion to study the extendable subgroup of the mapping class group of the knotted torus.
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Taxonomy
TopicsGeometric and Algebraic Topology · Computational Geometry and Mesh Generation