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On
the homology of the space of knots
Ryan Budney and Fred Cohen |
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Geometry & Topology 13 (2009) 99–139
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Abstract |
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Consider the space of long knots in , . This is the space of knots as studied by V Vassiliev. Based on previous work [Budney: Topology 46 (2007) 1–27], [Cohen, Lada and May: Springer Lecture Notes 533 (1976)] it follows that the rational homology of is free Gerstenhaber–Poisson algebra. A partial description of a basis is given here. In addition, the mod– homology of this space is a free, restricted Gerstenhaber–Poisson algebra. Recursive application of this theorem allows us to deduce that there is –torsion of all orders in the integral homology of . This leads to some natural questions about the homotopy type of the space of long knots in for , as well as consequences for the space of smooth embeddings of in and embeddings of in . |
Keywords
knots, embeddings, spaces, cubes, homology
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Mathematical Subject Classification 2000
Primary: 58D10, 57T25
Secondary: 57M25, 57Q45
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References |
Publication
Received: 2 July 2008
Revised: 14 September 2008
Accepted: 4 September 2008
Preview posted: 22 October 2008
Published: 1 January 2009
Proposed: John Morgan
Seconded: Ralph Cohen, Steve Ferry
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Authors |
| Ryan Budney | |
| Department of Mathematics and
Statistics University of Victoria Victoria BC Canada V8W 3P4 |
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| Fred Cohen | |
| Department of Mathematics University of Rochester Rochester NY 14627 USA |
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