- Basic Info -

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

- Papers -

- [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]

- Referrence Books -

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

- DRG Description -

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.

- Schedule -

- 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: