中科院数学与系统科学研究院
数学研究所
拓扑研讨班
报告人： 苏桃 博士（清华大学）
题 目：Augmentations from Legendrian knots
时 间：2021.11.10（星期三），14:30-15 :30
地 点：南楼N802室
摘 要：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.
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