Work

Embedding spaces of split links

Year: 2025

Type: article

Abstract: We study the homotopy type of the space E (L) of un-parametrised embeddings of a split link L = L1 ... Ln in R3. Our main result is a simple description of the fundamental group, or motion group, of E (L), and we extend this to a description of the motion group of embeddings in S3. The main tool we build is a semi-simplicial space of separating systems, which we show is homotopy equivalent to E (L). This combinatorial object provides a gateway to studying the homotopy type of E (L) via the homotopy type of the spaces E (Li).

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2025.110235

Authors: Rachael Boyd, Corey Bregman

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790