Homotopy Bott-Taubes integrals and the Taylor tower for the space of knots

Details Homotopy Bott-Taubes integrals and the Taylor tower for the space of knots Homotopy Bott-Taubes integrals and the Taylor tower for the space of knots

2011-02-11

arxiv.org/abs/1102.2270v1

Mathematics

Algebraic Topology

25 pages

Scientific paper

This work continues the study of a homotopy-theoretic construction of the author inspired by the Bott-Taubes integrals. Bott and Taubes constructed knot invariants by integrating differential forms along the fiber of a bundle over the space of knots in R^3. Their techniques were later used to construct real cohomology classes in the space of knots in R^d, d>3. By doing this integration via a Pontrjagin-Thom construction, the author constructed cohomology classes in the knot space with arbitrary coefficients. Here we carry out the construction over the stages of the Taylor tower for the knot space, which arises from the Goodwillie-Weiss embedding calculus. We work both over the totalization of Sinha's cosimplicial model and directly over the stages of the Taylor tower.

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