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

作者：Koytcheff Robin^*

来源：Journal of Homotopy and Related Structures, 2016, 11(3): 443-467.

DOI：10.1007/s40062-015-0112-0

• Spaces of knots and links
• Configuration space integrals
• Embedding calculus
• Pontrjagin-Thom constructions
• Finite-type invariants of knots and links
• Milnor triple linking number

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 . Their techniques were later used by Cattaneo et al. to construct real "Vassiliev-type" cohomology classes in the space of knots in , . By doing this integration via a Pontrjagin-Thom construction, we constructed cohomology classes in the knot space with arbitrary coefficients. We later showed that a refinement of this construction recovers the Milnor triple linking number for string links. We conjecture that we can produce all Vassiliev-type classes in this manner. Here we extend our homotopy-theoretic constructions to the stages of the Taylor tower for the embedding space, which arises from the Goodwillie-Weiss embedding calculus. We use the model of "punctured knots and links" for the Taylor tower.

• 出版日期2016-9