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