Work

Minimal generating sets and the abelianization for the quasitoric braid group

Year: 2024

Type: article

Abstract: A toric braid is a braid whose closure is a torus link in [Formula: see text]. Manturov [A combinatorial representation of links by quasitoric braids, European J. Combin. 23(2) (2002) 207–212] generalized toric braids that is called quasitoric braids and showed that the subset of quasitoric braids in the classical braid group is a subgroup of the braid group. We call this subgroup the quasitoric braid group. In this paper, we give two minimal generating sets for the quasitoric braid group and determine its abelianization. The minimalities of these two generating sets are obtained from a lower bound by the number of generators for the abelianization.

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216524500469

Author: Genki Omori

Institution: Shibaura Institute of Technology

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

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