Finite type knot invariants and calculus of functors

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We associate a Taylor tower supplied by 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.
Revised; to appear in Compositio Mathematica

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Algebraic Topology, Geometric Topology, 57R40; 57M27

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http://salesiana.dossiersoluciones.com/handle/123456789/70022

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0401440
 http://arxiv.org/abs/math/0401440

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arXiv