Volume 17, issue 3 (2017)

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The augmentation category map induced by exact Lagrangian cobordisms

Yu Pan

Algebraic & Geometric Topology 17 (2017) 1813–1870
Bibliography
1 J A Baldwin, S Sivek, Invariants of Legendrian and transverse knots in monopole knot homology, preprint (2014) arXiv:1405.3275
2 F Bourgeois, B Chantraine, Bilinearized Legendrian contact homology and the augmentation category, J. Symplectic Geom. 12 (2014) 553 MR3248668
3 F Bourgeois, J M Sabloff, L Traynor, Lagrangian cobordisms via generating families: construction and geography, Algebr. Geom. Topol. 15 (2015) 2439 MR3402346
4 B Chantraine, Lagrangian concordance of Legendrian knots, Algebr. Geom. Topol. 10 (2010) 63 MR2580429
5 B Chantraine, Lagrangian concordance is not a symmetric relation, Quantum Topol. 6 (2015) 451 MR3392961
6 B Chantraine, G Dimitroglou Rizell, P Ghiggini, R Golovko, Floer homology and Lagrangian concordance, from: "Proceedings of the Gökova Geometry–Topology Conference" (editors S Akbulut, D Auroux, T Önder), GGT (2015) 76 MR3381440
7 Y Chekanov, Differential algebra of Legendrian links, Invent. Math. 150 (2002) 441 MR1946550
8 Y V Chekanov, Invariants of Legendrian knots, from: "Proceedings of the International Congress of Mathematicians, II" (editor T Li), Higher Ed. Press (2002) 385 MR1957049
9 W Chongchitmate, L Ng, An atlas of Legendrian knots, Exp. Math. 22 (2013) 26 MR3038780
10 G Civan, P Koprowski, J Etnyre, J M Sabloff, A Walker, Product structures for Legendrian contact homology, Math. Proc. Cambridge Philos. Soc. 150 (2011) 291 MR2770065
11 C Cornwell, L Ng, S Sivek, Obstructions to Lagrangian concordance, Algebr. Geom. Topol. 16 (2016) 797 MR3493408
12 G Dimitroglou Rizell, Exact Lagrangian caps and non-uniruled Lagrangian submanifolds, Ark. Mat. 53 (2015) 37 MR3319613
13 G Dimitroglou Rizell, Lifting pseudo-holomorphic polygons to the symplectisation of P × and applications, Quantum Topol. 7 (2016) 29 MR3459958
14 T Ekholm, Rational symplectic field theory over 2 for exact Lagrangian cobordisms, J. Eur. Math. Soc. 10 (2008) 641 MR2421157
15 T Ekholm, Rational SFT, linearized Legendrian contact homology, and Lagrangian Floer cohomology, from: "Perspectives in analysis, geometry, and topology" (editors I Itenberg, B Jöricke, M Passare), Progr. Math. 296, Springer (2012) 109 MR2884034
16 T Ekholm, J B Etnyre, J M Sabloff, A duality exact sequence for Legendrian contact homology, Duke Math. J. 150 (2009) 1 MR2560107
17 T Ekholm, J Etnyre, M Sullivan, The contact homology of Legendrian submanifolds in 2n+1, J. Differential Geom. 71 (2005) 177 MR2197142
18 T Ekholm, J Etnyre, M Sullivan, Orientations in Legendrian contact homology and exact Lagrangian immersions, Internat. J. Math. 16 (2005) 453 MR2141318
19 T Ekholm, K Honda, T Kálmán, Legendrian knots and exact Lagrangian cobordisms, J. Eur. Math. Soc. 18 (2016) 2627 MR3562353
20 T Ekholm, T Kálmán, Isotopies of Legendrian 1–knots and Legendrian 2–tori, J. Symplectic Geom. 6 (2008) 407 MR2471099
21 Y Eliashberg, Invariants in contact topology, Doc. Math. (1998) 327 MR1648083
22 Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, Geom. Funct. Anal. (2000) 560 MR1826267
23 J B Etnyre, L L Ng, J M Sabloff, Invariants of Legendrian knots and coherent orientations, J. Symplectic Geom. 1 (2002) 321 MR1959585
24 A Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988) 513 MR965228
25 E Getzler, J D S Jones, A–algebras and the cyclic bar complex, Illinois J. Math. 34 (1990) 256 MR1046565
26 B Keller, Introduction to A–infinity algebras and modules, Homology Homotopy Appl. 3 (2001) 1 MR1854636
27 C Leverson, Augmentations and rulings of Legendrian knots, J. Symplectic Geom. 14 (2016) 1089 MR3601885
28 M Menke, On the augmentation categories of positive braid closures, preprint (2015) arXiv:1509.09301
29 D Nadler, E Zaslow, Constructible sheaves and the Fukaya category, J. Amer. Math. Soc. 22 (2009) 233 MR2449059
30 L L Ng, Computable Legendrian invariants, Topology 42 (2003) 55 MR1928645
31 L Ng, D Rutherford, Satellites of Legendrian knots and representations of the Chekanov–Eliashberg algebra, Algebr. Geom. Topol. 13 (2013) 3047 MR3116313
32 L Ng, D Rutherford, V Shende, S Sivek, The cardinality of the augmentation category of a Legendrian link, preprint (2015) arXiv:1511.06724
33 L Ng, D Rutherford, V Shende, S Sivek, E Zaslow, Augmentations are sheaves, preprint (2015) arXiv:1502.04939
34 J M Sabloff, L Traynor, Obstructions to Lagrangian cobordisms between Legendrians via generating families, Algebr. Geom. Topol. 13 (2013) 2733 MR3116302
35 P Seidel, Fukaya categories and Picard–Lefschetz theory, Eur. Math. Soc. (2008) MR2441780
36 J D Stasheff, Homotopy associativity of H–spaces, I, Trans. Amer. Math. Soc. 108 (1963) 275 MR0158400
37 J D Stasheff, Homotopy associativity of H–spaces, II, Trans. Amer. Math. Soc. 108 (1963) 293 MR0158400