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Finite type knot invariants and the calculus of functors

Published online by Cambridge University Press:  13 January 2006

Ismar Volić
Ismar Volić
Affiliation:
Department of Mathematics, University of Virginia, Charlottesville, VA 22904-4137, USAismar@virginia.edu
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Abstract

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We associate a Taylor tower supplied by the calculus of the embedding functor to the space of long knots and study its cohomology spectral sequence. The combinatorics of the spectral sequence along the line of total degree zero leads to chord diagrams with relations as in finite type knot theory. We show that the spectral sequence collapses along this line and that the Taylor tower represents a universal finite type knot invariant.

Keywords

calculus of functorsfinite type invariantsVassiliev invariantsknotsspaces of knotsconfiguration spaces57R40 (primary)57M2757T35 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 1 , January 2006 , pp. 222 - 250
Copyright
Foundation Compositio Mathematica 2006