• Meetings: Tuesday 4-5 pm at 935 Evans Hall

• [E] Legendrian and Transverse Knots by John Etnyre, Handbook Of Knot Theory [pdf]
• [EES] Legendrian Contact Homology In P x R by Tobias Eckholm, John Etnyre, Michael G. Sullivan [arxiv]
• [G] Introduction to Legendrian Knots and Legendrian Contact Homology by Paulo Ghiggini [pdf]
• DRG Document (In Progress) [dropbox]

• [MS] Introduction To Symplectic Topology by Dusa McDuff & Dietmar Salamon, Oxford Mathematical Press
• [HG] Introduction To Contact Topology by Hansjorg Geiges, Cambridge Mathematical Press

This is the homepage for a research-oriented reading group in contact topology. The focus of the semester will be on non-contractible Legendrian sub-manifolds of contactizations of punctured symplectic surfaces. More precisely, we aim to write a paper providing detailed computational methods for and examples of linearized Legendrian contact homology. A broader goal is to conjecture very general vanishing or non-vanishing properties for these linearized homologies.

• Wk 1, 9.3-9.7: basics of Legendrian knots, classical invariants. p. 1-14 of [G], p.1-21 of [E]
• Wk 2, 9.10-9.14: basics of Legendrians continued. p.1-21 of [E]
• Wk 3, 9.17-9.21: dg-algebras, gradings, Legendrian contact dg-algebra. p. 14-28 of [G], p. 22-34 of [E]
• Wk 4, 9.24-9.28: linearization, augmentations for dg-algebras. linearized contact homology. p. 14-28 of [G], p. 22-34 of [E]
• Wk 5, 10.1-10.5: example computation: Chekanov knots
• Wk 6, 10.8-10.12: A-infinity structures on liearized homology.
• Wk 7, 10.15-10.19: Weinstein domains, Weinstein manifolds, deformations, contactizations.
• Wk 8, 10.22-10.26: Lagrangian/front projections in contactizations of surfaces. existence of legendrian lifts of immersed lagrangians/front diagrams.
• Wk 9, 10.29-11.2: Chekanov dg-algebra on surfaces: gradings.
• Wk 10, 11.5-11.9: Chekanov dg-algebra on surfaces: differential
• Wk 11, 11.12-11.16: computations for some non-contractible examples.
• Wk 12, 11.19-11.22: computations for some non-contractible examples continued.
• Wk 13, 11.26-11.30:
• Wk 14, 12.3-12.7:
• Wk 15, 12.10-12.14: