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, the 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. A number of these papers are part of the AIM preprint series.

Expository papers and slides from talks are available here.

arXiv PDF Topological strings, D-model, and knot contact homology
Joint with Mina Aganagic, Tobias Ekholm, and Cumrun Vafa. (April 2013)
Click on “More files”, to the right of this text, for the associated Mathematica notebook with augmentation varieties for links. More files

arXiv PDF On transverse invariants from Khovanov homology
Joint with Robert Lipshitz and Sucharit Sarkar. (March 2013)

arXiv PDF A topological introduction to knot contact homology
(October 2012)

arXiv PDF Satellites of Legendrian knots and representations of the Chekanov-Eliashberg algebra
Joint with Dan Rutherford.
Algebr. Geom. Topol., to appear.

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

Journal
arXiv PDF An atlas of Legendrian knots
Joint with Wutichai Chongchitmate.
Exp. Math. 22 (2013), no. 1, 26-37.
More files

Journal arXiv PDF Combinatorial knot contact homology and transverse knots
Adv. Math. 227 (2011), no. 6, 2189-2219. More files

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

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

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

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

Journal arXiv

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

Book arXiv

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
Framed knot contact homology
Duke Math. J. 141 (2008), no. 2, 365-406. More files

Journal
arXiv
Legendrian solid-torus links
Joint with Lisa Traynor.
J. Symplectic Geom. 2 (2005), no. 3, 411-443.

Journal arXiv

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

Journal arXiv

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

PS
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.

Back to Lenny Ng

	arXiv	PDF	Topological strings, D-model, and knot contact homology Joint with Mina Aganagic, Tobias Ekholm, and Cumrun Vafa. (April 2013) Click on “More files”, to the right of this text, for the associated Mathematica notebook with augmentation varieties for links.	More files
	arXiv	PDF	On transverse invariants from Khovanov homology Joint with Robert Lipshitz and Sucharit Sarkar. (March 2013)
	arXiv	PDF	A topological introduction to knot contact homology (October 2012)
	arXiv	PDF	Satellites of Legendrian knots and representations of the Chekanov-Eliashberg algebra Joint with Dan Rutherford. Algebr. Geom. Topol., to appear.
Journal	arXiv	PDF	Knot contact homology Joint with Tobias Ekholm, John Etnyre, and Michael Sullivan. Geom. Topol. 17 (2013), 975-1112.
Journal	arXiv	PDF	An atlas of Legendrian knots Joint with Wutichai Chongchitmate. Exp. Math. 22 (2013), no. 1, 26-37.	More files
Journal	arXiv	PDF	Combinatorial knot contact homology and transverse knots Adv. Math. 227 (2011), no. 6, 2189-2219.	More files
Journal	arXiv	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	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	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	PDF	Rational Symplectic Field Theory for Legendrian knots Invent. Math. 182 (2010), no. 3, 451-512.
Journal	arXiv	PDF	A family of transversely nonsimple knots Joint with Tirasan Khandhawit. Algebr. Geom. Topol. 10 (2010), no. 1, 293-314.
Journal	arXiv	PDF	A skein approach to Bennequin type inequalities Int. Math. Res. Not. 2008, Art. ID rnn116, 18 pp.
Journal	arXiv	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		A Legendrian Thurston-Bennequin bound from Khovanov homology Algebr. Geom. Topol. 5 (2005), 1637-1653.
Journal	arXiv		The correspondence between augmentations and rulings for Legendrian knots Joint with Josh Sabloff. Pacific J. Math. 224 (2006), no. 1, 141-150.
Book	arXiv		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		Framed knot contact homology Duke Math. J. 141 (2008), no. 2, 365-406.	More files
Journal	arXiv		Legendrian solid-torus links Joint with Lisa Traynor. J. Symplectic Geom. 2 (2005), no. 3, 411-443.
Journal	arXiv		Knot and braid invariants from contact homology II Geom. Topol. 9 (2005), 1603-1637.
Journal	arXiv		Knot and braid invariants from contact homology I Geom. Topol. 9 (2005), 247-297.	More files
		PS	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.