Embedding spaces of split links
Rachael Boyd, Corey Bregman

TL;DR
This paper characterizes the homotopy type of the space of unparametrised embeddings of split links in 3D space, providing a new combinatorial approach to understanding their fundamental groups and motion groups.
Contribution
It offers a simple description of the fundamental and motion groups of split link embedding spaces, extending to embeddings in the 3-sphere, using a novel semi-simplicial space of separating systems.
Findings
Homotopy equivalence between separating systems and embedding spaces
Explicit description of the fundamental group of embedding spaces
Extension of results to embeddings in the 3-sphere
Abstract
We study the homotopy type of the space of unparametrised embeddings of a split link in . Our main result is a simple description of the fundamental group, or motion group, of , and we extend this to a description of the motion group of embeddings in . The main tool we build is a semi-simplicial space of separating systems, which we show is homotopy equivalent to . This combinatorial object provides a gateway to studying the homotopy type of via the homotopy type of the spaces .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology
