Return to Colloquia & Seminar listing
Knot contact homology and the augmentation polynomial
Student-Run Geometry/Topology Seminar| Speaker: | Alex Takeda, UC Berkeley |
| Location: | 2112 MSB |
| Start time: | Tue, Mar 11 2014, 3:10PM |
Knot contact homology provides us a strong knot invariant, making distinctions between pairs of knots that are missed by many of the classical invariants. One can extract concrete invariants by considering augmentations of the differential graded algebra obtained by contact homology, and these can be used to define the augmentation variety and augmentation polynomial associated to the knot. This polynomial seems to encode a great deal of information from the contact homology, and is conjecturally closely related to other invariants such as the A-polynomial and the HOMFLY-PT polynomial.