A two-variable series for knot complements: recent developments and applications
Sergei Gukov (CALTECH - USA)
Abstract: In this talk, we review properties and applications of quantum link invariants constructed from infinite-dimensional representations of quantum groups at generic values of $q$. When these invariants were introduced by the speaker and Ciprian Manolescu approximately five years ago, they highlighted a new and surprising role of Spin$^c$ structures that was rather mysterious at the time and was not expected in complex Chern-Simons theory. Since then, the role of Spin$^c$ structures was understood thanks to many works --- including Akhmechet-Johnson-Krushkal, Moore-Tarasca, Harichurn-Nemethi-Svoboda, among others --- and plays an important part in connections to Heegaard Floer homology and categorification of quantum $U_q (sl_2)$ invariants of 3-manifolds at generic $q$. This opens a new path from quantum topology to the study of exotic smooth structures on 4-manifolds.
geometric topology
Audience: researchers in the topic
Series comments: Web-seminar series on Applications of Geometry and Topology
| Organizers: | Alicia Dickenstein, José-Carlos Gómez-Larrañaga, Kathryn Hess, Neza Mramor-Kosta, Renzo Ricca*, De Witt L. Sumners |
| *contact for this listing |