WorldCat Identities

Koytcheff, Robin Michael John

Works: 1 works in 1 publications in 1 language and 1 library holdings
Roles: Author
Publication Timeline
Most widely held works by Robin Michael John Koytcheff
A homotopy-theoretic view of Bott-Taubes integrals and knot spaces by Robin Michael John Koytcheff( )

1 edition published in 2010 in English and held by 1 WorldCat member library worldwide

We construct cohomology classes in the space of knots by considering a bundle over this space and "integrating along the fiber'' classes coming from the cohomology of configuration spaces using a Pontrjagin-Thom construction. The bundle we consider is essentially the one considered by Bott and Taubes, who integrated differential forms along the fiber to get knot invariants. By doing this "integration'' homotopy-theoretically, we are able to produce integral cohomology classes. Inspired by results of Budney and Cohen, we study how this integration is compatible with homology operations on the space of long knots. In particular we derive a product formula for evaluations of cohomology classes on homology classes, with respect to connect-sum of knots. We then adapt the construction to be compatible with tools coming from the Goodwillie-Weiss embedding calculus, in particular Sinha's cosimplicial model for the space of knots
Audience Level
Audience Level
  Kids General Special  
Audience level: 0.81 (from 0.81 for A homotopy ... to 0.81 for A homotopy ...)