Papers and preprints

This is an archive of work authored (or coauthored) by me, in reverse chronological order. Links to “official” journal/book web pages, arXiv, and local PDF copies are given where appropriate. Published versions may incorporate changes not present in arXiv and PDF versions, though I tried to minimize this when possible. Several papers have associated files (programs available for download, etc.) hosted on this site; click on “More files” for these.

For a succinct list of my arXiv papers, please see here. Expository papers and slides from talks are available here.

You can click on the box containing a paper's title to view (or hide) the paper's abstract.


arXiv:
1811.10966
PDF
Legendrian contact homology in R3
Joint with John Etnyre, November 2018.

Journal
arXiv:
1805.03603
PDF
Representations, sheaves, and Legendrian (2,m) torus links
Joint with Baptiste Chantraine and Steven Sivek.
J. London Math. Soc. (2) 100 (2019), 41-82.


arXiv:
1803.04011
PDF
Higher genus knot contact homology and recursion for colored HOMFLY-PT polynomials
Joint with Tobias Ekholm.
March 2018, arXiv:1803.04011.

Journal
arXiv:
1606.07050
PDF
A complete knot invariant from contact homology
Joint with Tobias Ekholm and Vivek Shende.
Invent. Math. 211 (2018), no. 3, 1149-1200.

Journal
arXiv:
1601.02167
PDF
Knot contact homology, string topology, and the cord algebra
Joint with Kai Cieliebak, Tobias Ekholm, and Janko Latschev.
J. Éc. polytech. Math.
4 (2017), 661-780.

Journal arXiv:
1511.06724
PDF
The cardinality of the augmentation category of a Legendrian link
Joint with Dan Rutherford, Vivek Shende, and Steven Sivek.
Math. Res. Lett. 24 (2017), no. 6, 1845-1874.


arXiv:
1502.04939
PDF
Augmentations are sheaves
Joint with Dan Rutherford, Vivek Shende, Steven Sivek, and Eric Zaslow.
Geom. Topol., to appear.

Journal
arXiv:
1411.1364
PDF
Obstructions to Lagrangian concordance
Joint with Chris Cornwell and Steven Sivek.
Algebr. Geom. Topol. 16 (2016), no. 2, 797-824.

Journal
arXiv:
1307.8436
PDF
Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold
Joint with Tobias Ekholm.
J. Differential Geom. 101 (2015), no. 1, 67-157.

Journal
arXiv:
1304.5778
PDF
Topological strings, D-model, and knot contact homology
Joint with Mina Aganagic, Tobias Ekholm, and Cumrun Vafa.
Adv. Theor. Math. Phys. 18 (2014), no. 4, 827-956.
Click on “More files”, to the right of this text, for the associated Mathematica notebook with augmentation varieties for links.
More files
Journal
arXiv:
1303.6371
PDF
On transverse invariants from Khovanov homology
Joint with Robert Lipshitz and Sucharit Sarkar.
Quantum Topol. 6 (2015), no. 3, 475-513.

Book
arXiv:
1210.4803
PDF
A topological introduction to knot contact homology
In Contact and Symplectic Topology, Bolyai Soc. Math. Stud. 26 (Springer, Berlin, 2014).

Journal
arXiv:
1206.2259
PDF
Satellites of Legendrian knots and representations of the Chekanov-Eliashberg algebra
Joint with Dan Rutherford.
Algebr. Geom. Topol. 13 (2013), no. 5, 3047-3097.

Journal
arXiv:
1109.1542
PDF
Knot contact homology
Joint with Tobias Ekholm, John Etnyre, and Michael Sullivan.
Geom. Topol. 17 (2013), 975-1112.

Journal
arXiv:
1010.3997
PDF
An atlas of Legendrian knots
Joint with Wutichai Chongchitmate.
Exp. Math. 22 (2013), no. 1, 26-37.
More files
Journal arXiv:
1010.0451
PDF
Combinatorial knot contact homology and transverse knots
Adv. Math. 227 (2011), no. 6, 2189-2219.
More files
Journal arXiv:
1010.0450
PDF
Filtrations on the knot contact homology of transverse knots
Joint with Tobias Ekholm, John Etnyre, and Michael Sullivan.
Math. Ann. 355 (2013), no. 4, 1561-1591.

Journal
arXiv:
1002.2400
PDF
Legendrian and transverse twist knots
Joint with John Etnyre and Vera Vértesi.
J. Eur. Math. Soc. (JEMS) 15 (2013), no. 3, 969-995.

Book
arXiv:
0812.3665
PDF
Grid diagrams, braids, and contact geometry
Joint with Dylan Thurston.
Proceedings of Gökova Geometry-Topology Conference 2008, 120-136 (Gökova Geometry-Topology Conference (GGT), Gökova, 2009). 

Journal arXiv:
0806.4598

PDF
Rational Symplectic Field Theory for Legendrian knots
Invent. Math. 182 (2010), no. 3, 451-512. 

Journal
arXiv:
0806.1887

PDF
A family of transversely nonsimple knots
Joint with Tirasan Khandhawit.
Algebr. Geom. Topol. 10 (2010), no. 1, 293-314.

Journal
arXiv:
0709.2141

PDF
A skein approach to Bennequin type inequalities
Int. Math. Res. Not. 2008, Art. ID rnn116, 18 pp. 

Journal
arXiv:
0703.5446

PDF
Transverse knots distinguished by knot Floer homology
Joint with Peter Ozsváth and Dylan Thurston.
J. Symplectic Geom. 6 (2008), no. 4, 461-490. 
More files
Journal
arXiv PDF
On arc index and maximal Thurston-Bennequin number
J. Knot Theory Ramifications 21 (2012), no. 4, 1250031, 11 pp.

Journal
arXiv PDF
A Legendrian Thurston-Bennequin bound from Khovanov homology
Algebr. Geom. Topol. 5 (2005), 1637-1653. 

Journal arXiv
PDF
The correspondence between augmentations and rulings for Legendrian knots
Joint with Josh Sabloff.
Pacific J. Math. 224 (2006), no. 1, 141-150. 

Book arXiv
PDF
Plane curves and contact geometry
In Proceedings of 12th Gökova Geometry-Topology Conference, ed. S. Akbulut, T. Önder, and R. J. Stern (International Press, 2006), 165-174. 

Book arXiv

Conormal bundles, contact homology, and knot invariants
In The Interaction of finite-type and Gromov-Witten invariants at the Banff International Research Station (2003), Geom. Topol. Monogr. 8 (2006), 129-144.

Journal
arXiv PDF
Framed knot contact homology
Duke Math. J. 141 (2008), no. 2, 365-406. 
More files
Journal arXiv PDF
Legendrian solid-torus links
Joint with Lisa Traynor.
J. Symplectic Geom. 2 (2005), no. 3, 411-443.

Journal arXiv
PDF
Knot and braid invariants from contact homology II
Geom. Topol. 9 (2005), 1603-1637. 

Journal arXiv
PDF
Knot and braid invariants from contact homology I
Geom. Topol. 9 (2005), 247-297.
More files


PDF
Problems in low dimensional contact geometry
Joint with John Etnyre.
In Topology and Geometry of Manifolds, Proc. Sympos. Pure Math. 71 (2003), 337-357, the proceedings of the 2001 Georgia International Topology Conference.


arXiv
The Legendrian satellite construction
The key portions of this paper are now incorporated into “Legendrian solid-torus links” above.



PDF
Invariants of Legendrian links
My Ph.D. dissertation, April 2001. Many of the main results are included in “Computable Legendrian invariants,” “The Legendrian satellite construction,” and “Maximal Thurston-Bennequin number of two-bridge links,” found elsewhere on this page. One other result which might be of interest is a calculation of maximal Thurston-Bennequin number for many pretzel knots.

Journal arXiv
Invariants of Legendrian knots and coherent orientations
With John Etnyre and Josh Sabloff.
J. Symplectic Geom. 1 (2002), no. 2, 321-367.
The latest arXiv version incorporates some corrections to the published version. A list of just these corrections is available here.

Journal
arXiv
Computable Legendrian invariants
Topology 42 (2003), no. 1, 55-82.
Caution: the published version is more up-to-date than the arXiv version.

Journal arXiv

Maximal Thurston-Bennequin number of two-bridge links
Algebr. Geom. Topol. 1 (2001), 427-434.
There is a typographical error in the table at the end of the paper (p. 433): the row for 915 should be -1,-10 rather than -10,-1.


arXiv
Legendrian mirrors and Legendrian isotopy
A slightly different approach to a result also proven in “Computable Legendrian invariants,” above.



PDF
The rook on the half-chessboard, or how not to diagonalize a matrix
With Kiran Kedlaya.
Amer. Math. Monthly 105 (1998), no. 9, 819-824.



PDF
Heisenberg model, Bethe ansatz, and random walks
My undergraduate senior thesis, spring 1996, written under the direction of Persi Diaconis.

Journal

Hamiltonian decomposition of lexicographic products of digraphs
J. Combin. Theory Ser. B 73 (1998), no. 2, 119-129.
From research conducted in the 1995 Duluth REU summer program.

Journal

Hamiltonian decomposition of complete regular multipartite digraphs
Discrete Math. 177 (1997), no. 1-3, 279-285.
From the 1995 Duluth REU.

Journal

k-ordered hamiltonian graphs
J. Graph Theory 24 (1997), no. 1, 45-57.
With Michelle Schultz.
From the 1994 Duluth REU. This paper gives me Erdös number 3: Michelle Schultz, Gary Chartrand, Paul Erdös.

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