Geometry & Topology Volume 27, issue 6 (2023)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Duality between Lagrangian and Legendrian invariants

Tobias Ekholm and Yankı Lekili

Geometry & Topology 27 (2023) 2049–2179

DOI: 10.2140/gt.2023.27.2049

Bibliography

1	M Abouzaid, Morse homology, tropical geometry, and homological mirror symmetry for toric varieties, Selecta Math. 15 (2009) 189 MR2529936
2	M Abouzaid, On the wrapped Fukaya category and based loops, J. Symplectic Geom. 10 (2012) 27 MR2904032
3	M Abouzaid, P Seidel, An open string analogue of Viterbo functoriality, Geom. Topol. 14 (2010) 627 MR2602848
4	J F Adams, On the cobar construction, Proc. Nat. Acad. Sci. U.S.A. 42 (1956) 409 MR79266
5	J F Adams, P J Hilton, On the chain algebra of a loop space, Comment. Math. Helv. 30 (1956) 305 MR77929
6	M Aganagic, T Ekholm, L Ng, C Vafa, Topological strings, D–model, and knot contact homology, Adv. Theor. Math. Phys. 18 (2014) 827 MR3277674
7	J F Barraud, O Cornea, Lagrangian intersections and the Serre spectral sequence, Ann. of Math. 166 (2007) 657 MR2373371
8	A Beilinson, V Ginzburg, W Soergel, Koszul duality patterns in representation theory, J. Amer. Math. Soc. 9 (1996) 473 MR1322847
9	J M Boardman, Conditionally convergent spectral sequences, from: "Homotopy invariant algebraic structures" (editors J P Meyer, J Morava, W S Wilson), Contemp. Math. 239, Amer. Math. Soc. (1999) 49 MR1718076
10	F Bourgeois, B Chantraine, Bilinearized Legendrian contact homology and the augmentation category, J. Symplectic Geom. 12 (2014) 553 MR3248668
11	F Bourgeois, T Ekholm, Y Eliashberg, Effect of Legendrian surgery, Geom. Topol. 16 (2012) 301 MR2916289
12	F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder, Compactness results in symplectic field theory, Geom. Topol. 7 (2003) 799 MR2026549
13	E H Brown Jr., Twisted tensor products, I, Ann. of Math. 69 (1959) 223 MR105687
14	G Carlsson, R J Milgram, Stable homotopy and iterated loop spaces, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 505 MR1361898
15	R Casals, E Murphy, Legendrian fronts for affine varieties, Duke Math. J. 168 (2019) 225 MR3909897
16	K T Chen, Iterated path integrals, Bull. Amer. Math. Soc. 83 (1977) 831 MR454968
17	K Cieliebak, T Ekholm, J Latschev, Compactness for holomorphic curves with switching Lagrangian boundary conditions, J. Symplectic Geom. 8 (2010) 267 MR2684508
18	K Cieliebak, Y Eliashberg, Flexible Weinstein manifolds, from: "Symplectic, Poisson, and noncommutative geometry" (editors T Eguchi, Y Eliashberg), Math. Sci. Res. Inst. Publ. 62, Cambridge Univ. Press (2014) 1 MR3380672
19	K Cieliebak, J Latschev, The role of string topology in symplectic field theory, from: "New perspectives and challenges in symplectic field theory" (editors M Abreu, F Lalonde, L Polterovich), CRM Proc. Lecture Notes 49, Amer. Math. Soc. (2009) 113 MR2555935
20	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
21	S Eilenberg, J C Moore, Limits and spectral sequences, Topology 1 (1962) 1 MR148723
22	T Ekholm, Morse flow trees and Legendrian contact homology in 1–jet spaces, Geom. Topol. 11 (2007) 1083 MR2326943
23	T Ekholm, Rational symplectic field theory over ℤ₂ for exact Lagrangian cobordisms, J. Eur. Math. Soc. 10 (2008) 641 MR2421157
24	T Ekholm, A version of rational SFT for exact Lagrangian cobordisms in 1–jet spaces, from: "New perspectives and challenges in symplectic field theory" (editors M Abreu, F Lalonde, L Polterovich), CRM Proc. Lecture Notes 49, Amer. Math. Soc. (2009) 173 MR2555937
25	T Ekholm, Holomorphic curves for Legendrian surgery, preprint (2019) arXiv:1906.07228
26	T Ekholm, J B Etnyre, L Ng, M G Sullivan, Knot contact homology, Geom. Topol. 17 (2013) 975 MR3070519
27	T Ekholm, J Etnyre, M Sullivan, Orientations in Legendrian contact homology and exact Lagrangian immersions, Internat. J. Math. 16 (2005) 453 MR2141318
28	T Ekholm, J Etnyre, M Sullivan, Legendrian contact homology in P × ℝ, Trans. Amer. Math. Soc. 359 (2007) 3301 MR2299457
29	T Ekholm, K Honda, T Kálmán, Legendrian knots and exact Lagrangian cobordisms, J. Eur. Math. Soc. (JEMS) 18 (2016) 2627 MR3562353
30	T Ekholm, A Oancea, Symplectic and contact differential graded algebras, Geom. Topol. 21 (2017) 2161 MR3654106
31	T Ekholm, I Smith, Exact Lagrangian immersions with one double point revisited, Math. Ann. 358 (2014) 195 MR3157996
32	T Etgü, Y Lekili, Koszul duality patterns in Floer theory, Geom. Topol. 21 (2017) 3313 MR3692968
33	Y Félix, J C Thomas, Extended Adams–Hilton’s construction, Pacific J. Math. 128 (1987) 251 MR888517
34	K Fukaya, Application of Floer homology of Langrangian submanifolds to symplectic topology, from: "Morse theoretic methods in nonlinear analysis and in symplectic topology" (editors P Biran, O Cornea, F Lalonde), NATO Sci. Ser. II Math. Phys. Chem. 217, Springer (2006) 231 MR2276953
35	K Fukaya, Y G Oh, Zero-loop open strings in the cotangent bundle and Morse homotopy, Asian J. Math. 1 (1997) 96 MR1480992
36	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory : anomaly and obstruction, I, 46, Amer. Math. Soc. (2009) MR2553465
37	P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
38	M Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
39	E Herscovich, Hochschild (co)homology and Koszul duality, preprint (2014) arXiv:1405.2247
40	J V S Holstein, Morita cohomology, PhD thesis, University of Cambridge (2014)
41	J V S Holstein, Morita cohomology, Math. Proc. Cambridge Philos. Soc. 158 (2015) 1 MR3300312
42	J D S Jones, Cyclic homology and equivariant homology, Invent. Math. 87 (1987) 403 MR870737
43	M Kalck, D Yang, Relative singularity categories, I : Auslander resolutions, Adv. Math. 301 (2016) 973 MR3539395
44	D M Kan, Abstract homotopy, IV, Proc. Nat. Acad. Sci. U.S.A. 42 (1956) 542 MR87938
45	B Keller, Deriving DG categories, Ann. Sci. École Norm. Sup. 27 (1994) 63 MR1258406
46	M Kontsevich, Symplectic geometry of homological algebra, preprint (2009)
47	K Lefèvre-Hasegawa, Sur les A_∞–catègories, PhD thesis, Université Paris 7 (2003) arXiv:math/0310337
48	Y Lekili, A Polishchuk, Arithmetic mirror symmetry for genus 1 curves with n marked points, Selecta Math. 23 (2017) 1851 MR3663596
49	J L Loday, B Vallette, Algebraic operads, 346, Springer (2012) MR2954392
50	D M Lu, J H Palmieri, Q S Wu, J J Zhang, Koszul equivalences in A_∞–algebras, New York J. Math. 14 (2008) 325 MR2430869
51	J McCleary, User’s guide to spectral sequences, 12, Publish or Perish (1985) MR820463
52	J Milnor, Morse theory, 51, Princeton Univ. Press (1963) MR0163331
53	D Nadler, Wrapped microlocal sheaves on pairs of pants, preprint (2016) arXiv:1604.00114
54	J A Neisendorfer, What is loop multiplication anyhow?, J. Homotopy Relat. Struct. 12 (2017) 659 MR3691300
55	L Ng, D Rutherford, V Shende, S Sivek, E Zaslow, Augmentations are sheaves, Geom. Topol. 24 (2020) 2149 MR4194293
56	L Positselski, Two kinds of derived categories, Koszul duality, and comodule–contramodule correspondence, 996, Amer. Math. Soc. (2011) MR2830562
57	A Prouté, A_∞–structures : modèles minimaux de Baues–Lemaire et Kadeishvili et homologie des fibrations, Repr. Theory Appl. Categ. (2011) 1 MR2844537
58	S Schwede, B Shipley, Equivalences of monoidal model categories, Algebr. Geom. Topol. 3 (2003) 287 MR1997322
59	P Seidel, Fukaya categories and Picard–Lefschetz theory, Eur. Math. Soc. (2008) MR2441780
60	J P Serre, Homologie singulière des espaces fibrés : applications, Ann. of Math. 54 (1951) 425 MR45386
61	Z Sylvan, Partially wrapped Floer theory, talk (2016)
62	Z Sylvan, On partially wrapped Fukaya categories, J. Topol. 12 (2019) 372 MR3911570
63	G Tabuada, Theorie homotopique des DG–categories, preprint (2007) arXiv:0710.4303
64	C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324