Work

Distinguishing 2-knots admitting circle actions by fundamental groups

Year: 2024

Type: book-chapter

Abstract: A 2-sphere embedded in the 4-sphere invariant under a circle action is called a branched twist spin. A branched twist spin is constructed from a 1-knot in the 3-sphere and a pair of coprime integers uniquely. In this paper, we study, for each pair of coprime integers, if two different 1-knots yield the same branched twist spin, and prove that such a pair of 1-knots does not exist in most cases. Fundamental groups of 3-orbifolds of cyclic type are obtained as quotient groups of the fundamental groups of the complements of branched twist spins. We use these groups for distinguishing branched twist spins.

Source: Revista Matemática Complutense

DOI: 10.1007/s13163-024-00504-6

Authors: Mizuki Fukuda, Masaharu Ishikawa

Institutions: Tohoku University, National Institute of Advanced Industrial Science and Technology, Keio University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Japan Society for the Promotion of Science