On the homology of the space of knots

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dc.creatorBudney, Ryan
dc.creatorCohen, Frederick
dc.date2005-04-10
dc.date2008-11-14
dc.date.accessioned2026-07-07T10:18:06Z
dc.date.available2026-07-07T10:18:06Z
dc.descriptionConsider the space of `long knots' in R^n, K_{n,1}. This is the space of knots as studied by V. Vassiliev. Based on previous work of the authors, it follows that the rational homology of K_{3,1} is free Gerstenhaber-Poisson algebra. A partial description of a basis is given here. In addition, the mod-p homology of this space is a `free, restricted Gerstenhaber-Poisson algebra'. Recursive application of this theorem allows us to deduce that there is p-torsion of all orders in the integral homology of K_{3,1}. This leads to some natural questions about the homotopy type of the space of long knots in R^n for n>3, as well as consequences for the space of smooth embeddings of S^1 in S^3.
dc.description36 pages, 6 figures. v3: small revisions before publication
dc.identifierhttps://arxiv.org/abs/math/0504206
dc.identifierhttp://arxiv.org/abs/math/0504206
dc.identifierGeometry & Topology 13 (2009) 99--139
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174078
dc.subjectGeometric Topology
dc.subjectAlgebraic Topology
dc.subjectQuantum Algebra
dc.subject58D10; 57T25; 57M25; 57Q45
dc.titleOn the homology of the space of knots
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