Hold Date

2022-12-23 17:00〜2022-12-23 18:00

Place

C-512

Object person

　

Speaker

Keiichi Sakai (Shinshu University)

Abstract:
It is known that the Vassiliev invariants for (long) knots can be described as the integrations over the configuration spaces associated with trivalent graph cocycles (R. Bott-C. Taubes, T. Kohno), while non-trivalent graph cocycles yield positive degree cocycles of the space of (long) knots (A. Cattaneo-P. Cotta-Ramusino-R. Longoni). The integrations of some concrete graph cocycles over the Gramain cycle and the Fox-Hatcher cycle are known to produce some Vassiliev invariants (V. Turchin, R. Longoni, K. Pelatt-D. Sinha, A. Mortier). I'd like to explain an approach to generalize these facts from the viewpoint of configuration space integrals. This talk is based on joint work with Saki Kanou that gives a Vassiliev invariants of order three.