Reading course on Khovanov homology

This is an informal reading course on Khovanov homology and low-dimensional topology in Fall 2020.
Older notes: Winter-Spring 2020 .
Organizers: Roger Casals , Eugene Gorsky , Laura Starkston .
The seminar meets on Thursdays at 1-2pm.


10/1 Introductory meeting: notes

10/8 Eugene: recap of Khovanov homology [BN] notes

10/15 Yukun: intro to contact topology notes

10/22 Yukun continues notes

10/29 James: Markov theorem for transversal links. notes

11/5 Tonie: annular Khovanov homology. Notes: part 1, part 2

11/12 Shanon: open book decompositions notes
Etnyre's lectures on open books: 1 , 2 , 3

11/19 Neetal: Annular Khovanov-Lee homology, braids, and cobordisms. Notes

12/3 Ian: Categorified invariants and the braid group+Plamenevskaya invariant.
Notes: part 1 , part 2

Course materials

Annular Khovanov homology
  1. D. Bar-Natan. On Khovanov's categorification of the Jones polynomial. arXiv:math/0201043 [Eugene]
  2. R. Akhmechet. Equivariant annular Khovanov homology. slides
  3. J. Elisenda Grigsby, Anthony M. Licata, Stephan M. Wehrli. Annular Khovanov-Lee homology, braids, and cobordisms. arXiv:1612.05953 [Neetal]
  4. J. Elisenda Grigsby, Stephan M. Wehrli. Khovanov homology, sutured Floer homology, and annular links. arxiv:0907.4375 [Tonie]
  5. John A. Baldwin, J. Elisenda Grigsby. Categorified invariants and the braid group. arxiv:1212.2222 [Ian Sullivan]
  6. J. Elisenda Grigsby, Yi Ni. Sutured Khovanov homology distinguishes braids from other tangles. arXiv:1305.2183
Introduction to contact geometry
  1. John B. Etnyre. Lectures on Contact Geometry in Low-Dimensional Topology. arXiv:0610798 [Yukun]
  2. John B. Etnyre. Lectures on open book decompositions and contact structures. arXiv:0409402 [Shanon]
  3. John B. Etnyre. Legendrian and Transversal Knots. arXiv:0306256
Interaction between contact geometry and Khovanov homology
  1. Stepan Orevkov and V. Shevchishin. Markov theorem for transversal links. J. of Knot Theory and Ramifications, 12(2003), 905-913 [James]
  2. Olga Plamenevskaya. Transverse knots and Khovanov homology. arxiv:0412184
  3. Robert Lipshitz, Lenhard Ng, Sucharit Sarkar. On transverse invariants from Khovanov homology. arXiv:1303.6371
  4. John A. Baldwin, Olga Plamenevskaya. Khovanov homology, open books, and tight contact structures. arXiv:0808.2336