Algebraic & Geometric Topology Volume 22, issue 5 (2022)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Augmentations and ruling polynomials for Legendrian graphs

Byung Hee An, Youngjin Bae and Tao Su

Algebraic & Geometric Topology 22 (2022) 2079–2185

DOI: 10.2140/agt.2022.22.2079

Bibliography

1	B H An, Y Bae, A Chekanov–Eliashberg algebra for Legendrian graphs, J. Topol. 13 (2020) 777 MR4092780
2	B H An, Y Bae, T Kálmán, Ruling invariants for Legendrian graphs, preprint (2019) arXiv:1911.08668
3	B H An, Y Bae, S Kim, Legendrian singular links and singular connected sums, J. Symplectic Geom. 16 (2018) 885 MR3917723
4	B H An, Y Bae, T Su, Augmentations are sheaves for Legendrian graphs, (2019) arXiv:1912.10782
5	S Baader, M Ishikawa, Legendrian graphs and quasipositive diagrams, Ann. Fac. Sci. Toulouse Math. 18 (2009) 285 MR2562830
6	S A Barannikov, The framed Morse complex and its invariants, from: "Singularities and bifurcations" (editor V I Anold), Adv. Soviet Math. 21, Amer. Math. Soc. (1994) 93 MR1310596
7	Y Chekanov, Differential algebra of Legendrian links, Invent. Math. 150 (2002) 441 MR1946550
8	T Ekholm, L Ng, Legendrian contact homology in the boundary of a subcritical Weinstein 4–manifold, J. Differential Geom. 101 (2015) 67 MR3356070
9	Y Eliashberg, M Fraser, Topologically trivial Legendrian knots, J. Symplectic Geom. 7 (2009) 77 MR2496415
10	Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, Geom. Funct. Anal. (2000) 560 MR1826267
11	J B Etnyre, Lectures on open book decompositions and contact structures, from: "Floer homology, gauge theory, and low-dimensional topology" (editors D A Ellwood, P S Ozsváth, A I Stipsicz, Z Szabó), Clay Math. Proc. 5, Amer. Math. Soc. (2006) 103 MR2249250
12	J B Etnyre, L L Ng, J M Sabloff, Invariants of Legendrian knots and coherent orientations, J. Symplectic Geom. 1 (2002) 321 MR1959585
13	Y Félix, S Halperin, J C Thomas, Rational homotopy theory, 205, Springer (2001) MR1802847
14	H Geiges, An introduction to contact topology, 109, Cambridge Univ. Press (2008) MR2397738
15	E Giroux, Géométrie de contact : de la dimension trois vers les dimensions supérieures, from: "Proceedings of the International Congress of Mathematicians, II" (editor T Li), Higher Ed. Press (2002) 405 MR1957051
16	T Hausel, F Rodriguez-Villegas, Mixed Hodge polynomials of character varieties, Invent. Math. 174 (2008) 555 MR2453601
17	M B Henry, D Rutherford, Ruling polynomials and augmentations over finite fields, J. Topol. 8 (2015) 1 MR3335247
18	V F R Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. 12 (1985) 103 MR766964
19	D Nadler, Arboreal singularities, Geom. Topol. 21 (2017) 1231 MR3626601
20	L L Ng, Computable Legendrian invariants, Topology 42 (2003) 55 MR1928645
21	L Ng, D Rutherford, V Shende, S Sivek, E Zaslow, Augmentations are sheaves, Geom. Topol. 24 (2020) 2149 MR4194293
22	D O’Donnol, E Pavelescu, On Legendrian graphs, Algebr. Geom. Topol. 12 (2012) 1273 MR2966686
23	Y Pan, D Rutherford, Functorial LCH for immersed Lagrangian cobordisms, J. Symplectic Geom. 19 (2021) 635 MR4325415
24	V Shende, D Treumann, H Williams, E Zaslow, Cluster varieties from Legendrian knots, Duke Math. J. 168 (2019) 2801 MR4017516
25	T Su, Ruling polynomials and augmentations for Legendrian tangles, preprint (2017) arXiv:1707.04948
26	T Su, A Hodge-theoretic study of augmentation varieties associated to Legendrian knots/tangles, PhD thesis, University of California, Berkeley (2018)