Homotopy Bott-taubes integrals and the Milnor triple linking number
Vortrag von Dr. Robin Koytcheff
Sprecher eingeladen von: Prof. Dr. Alberto Cattaneo
Datum: 31.01.13 Zeit: 15.15 - 16.15 Raum: Y27H12
Abstract: Bott and Taubes produced knot invariants by considering a bundle over the space of knots and integrating differential forms along its fiber. Their methods were used by D. Thurston to construct all Vassiliev invariants. They were also used by Cattaneo, Cotta-Ramusino, and Longoni to construct Vassiliev-type classes, which are real cohomology classes in spaces of knots in Euclidean space of dimension at least 4. By replacing integration of forms by a Pontrjagin–Thom construction, we can produce cohomology classes with arbitrary coefficients. We recover the Milnor triple linking number for string links via this method. Along the way, we find a description of this invariant as the degree of a certain map. More generally, we should be able to produce integral multiples of all the Vassiliev-type classes, showing that these classes are rational.