Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	苏桃博士，清华大学
Inviter:
Title:	Augmentations from Legendrian knots
Time & Venue:	2021.11.10 14:30-15:30 南楼N802室
Abstract:	In this talk, I will present a cut-and-glue approach in the study of augmentations associated to Legendrian knots. Given a Legendrian knot, this induces from relative contact homology a constructible co-sheaf of DGAs over the real line, whose global co-section recovers the Chekanov-Eliashberg DGA. It follows that, the augmentations of the Chekanov-Eliashberg DGA form the augmentation variety with a sheaf property. As an application, this gives naturally a cell decomposition for the augmentation variety. Consequently, we obtain a new proof to the formula that the E-polynomial of the variety is computed by the ruling polynomial, a combinatorially defined Legendrian isotopy invariant. Time permitting, I will also mention a second application in my recent work concerning part of the geometric P=W conjecture in nonabelian Hodge theory.