Embedding Spaces of Split Links
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Date
Authors
Volume
13
Issue
Journal
Series Titel
Oberwolfach Preprints (OWP)
Book Title
Publisher
Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach
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Abstract
We study the homotopy type of the space E(L) of unparametrised embeddings of a split link L=L1⊔…⊔Ln in R³. Inspired by work of Brendle and Hatcher, we introduce a semi-simplicial space of separating systems and show that this 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). We apply this tool to find a simple description of the fundamental group, or motion group, of E(L), and extend this to a description of the motion group of embeddings in S³.
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Keywords
Embedding spaces, Homotopy type, Semi-simplicial spaces, Split links, Motion groups
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This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.