Work

Groups generated by Dehn twists along fillings of surfaces

Year: 2025

Type: article

Abstract: Let [Formula: see text] denote a closed oriented surface of genus [Formula: see text]. A set [Formula: see text] of pairwise non-homotopic simple closed curves on [Formula: see text] such that [Formula: see text] and [Formula: see text] are in minimal position, is called a filling system or simply a filling of [Formula: see text], if [Formula: see text] is a disjoint union of [Formula: see text] topological discs for some [Formula: see text]. For [Formula: see text], let [Formula: see text] denote the Dehn twist along [Formula: see text]. In this paper, we show that for each [Formula: see text], there exists a filling [Formula: see text] of [Formula: see text] such that the group [Formula: see text] is isomorphic to the free group of rank [Formula: see text].

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216525500245

Author: Rakesh Kumar

Institution: Indian Institute of Technology Goa

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Council of Scientific and Industrial Research, India

Award: G2387986253