Geometry & Topology Volume 16, issue 1 (2012)

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Effect of Legendrian surgery

Frédéric Bourgeois, Tobias Ekholm and Yasha Eliashberg

Appendix: Sheel Ganatra and Maksim Maydanskiy

Geometry & Topology 16 (2012) 301–389

DOI: 10.2140/gt.2012.16.301

Bibliography

1	A Abbondandolo, M Schwarz, On the Floer homology of cotangent bundles, Comm. Pure Appl. Math. 59 (2006) 254 MR2190223
2	M Abouzaid, P Seidel, Altering symplectic manifolds by homologous recombination arXiv:1007.3281
3	M Abouzaid, P Seidel, An open string analogue of Viterbo functoriality, Geom. Topol. 14 (2010) 627 MR2602848
4	V I Arnol’d, Some remarks on symplectic monodromy of Milnor fibrations, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 99 MR1362824
5	I Assem, D Simson, A Skowroński, Elements of the representation theory of associative algebras. Vol. 1: Techniques of representation theory, London Math. Soc. Student Texts 65, Cambridge Univ. Press (2006) MR2197389
6	F Bourgeois, A Morse–Bott approach to contact homology, PhD thesis, Stanford University (2002)
7	F Bourgeois, T Ekholm, Y Eliashberg, Legendrian surgery triangles for contact and symplectic homology, in preparation
8	F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder, Compactness results in symplectic field theory, Geom. Topol. 7 (2003) 799 MR2026549
9	F Bourgeois, A Oancea, An exact sequence for contact- and symplectic homology, Invent. Math. 175 (2009) 611 MR2471597
10	Y Chekanov, Differential algebra of Legendrian links, Invent. Math. 150 (2002) 441 MR1946550
11	K Cieliebak, Subcritical Stein manifolds are split arXiv:math/0204351
12	K Cieliebak, Handle attaching in symplectic homology and the chord conjecture, J. Eur. Math. Soc. 4 (2002) 115 MR1911873
13	K Cieliebak, Y Eliashberg, Symplectic geometry of Stein manifolds, book in preparation
14	O Cornea, F Lalonde, Cluster homology arXiv:math/0508345
15	T Ekholm, Morse flow trees and Legendrian contact homology in $1$–jet spaces, Geom. Topol. 11 (2007) 1083 MR2326943
16	T Ekholm, Rational symplectic field theory over $\mathbb Z_2$ for exact Lagrangian cobordisms, J. Eur. Math. Soc. 10 (2008) 641 MR2421157
17	T Ekholm, J Etnyre, J M Sabloff, A duality exact sequence for Legendrian contact homology, Duke Math. J. 150 (2009) 1 MR2560107
18	T Ekholm, J Etnyre, M Sullivan, The contact homology of Legendrian submanifolds in $\mathbb{R}^{2n+1}$, J. Differential Geom. 71 (2005) 177 MR2197142
19	T Ekholm, J Etnyre, M Sullivan, Non-isotopic Legendrian submanifolds in $\mathbb R^{2n+1}$, J. Differential Geom. 71 (2005) 85 MR2191769
20	T Ekholm, J Etnyre, M Sullivan, Legendrian contact homology in $P\times\mathbb R$, Trans. Amer. Math. Soc. 359 (2007) 3301 MR2299457
21	T Ekholm, T Kálmán, Isotopies of Legendrian $1$–knots and Legendrian $2$–tori, J. Symplectic Geom. 6 (2008) 407 MR2471099
22	Y Eliashberg, Symplectic geometry of plurisubharmonic functions, from: "Gauge theory and symplectic geometry (Montreal, PQ, 1995)" (editors J Hurtubise, F Lalonde, G Sabidussi), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 488, Kluwer Acad. Publ. (1997) 49 MR1461569
23	Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, Geom. Funct. Anal. (2000) 560 MR1826267
24	Y Eliashberg, M Gromov, Convex symplectic manifolds, from: "Several complex variables and complex geometry, Part 2 (Santa Cruz, CA, 1989)" (editors E Bedford, J P D’Angelo, R E Greene, S G Krantz), Proc. Sympos. Pure Math. 52, Amer. Math. Soc. (1991) 135 MR1128541
25	A Floer, H Hofer, Symplectic homology I: Open sets in $\mathbb{C}^n$, Math. Z. 215 (1994) 37 MR1254813
26	U Frauenfelder, The Arnold–Givental conjecture and moment Floer homology, Int. Math. Res. Not. 2004 (2004) 2179 MR2076142
27	K Fukaya, Y G Oh, Zero-loop open strings in the cotangent bundle and Morse homotopy, Asian J. Math. 1 (1997) 96 MR1480992
28	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory: anomaly and obstruction. PartS I–II, AMS/IP Studies in Advanced Math. 46, American Math. Soc. (2009) MR2553465
29	K Fukaya, P Seidel, I Smith, The symplectic geometry of cotangent bundles from a categorical viewpoint, from: "Homological mirror symmetry" (editors A Kapustin, M Kreuzer, K G Schlesinger), Lecture Notes in Phys. 757, Springer (2009) 1 MR2596633
30	M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
31	H Hofer, K Wysocki, E Zehnder, A general Fredholm theory I: a splicing-based differential geometry, J. Eur. Math. Soc. 9 (2007) 841 MR2341834
32	H Hofer, K Wysocki, E Zehnder, A general Fredholm theory II: Implicit function theorems, Geom. Funct. Anal. 19 (2009) 206 MR2507223
33	H Hofer, K Wysocki, E Zehnder, A general Fredholm theory III: Fredholm functors and polyfolds, Geom. Topol. 13 (2009) 2279 MR2515707
34	M Maydanskiy, P Seidel, Lefschetz fibrations and exotic symplectic structures on cotangent bundles of spheres, J. Topol. 3 (2010) 157 MR2608480
35	M McLean, Lefschetz fibrations and symplectic homology, Geom. Topol. 13 (2009) 1877 MR2497314
36	J M Sabloff, Invariants of Legendrian knots in circle bundles, Commun. Contemp. Math. 5 (2003) 569 MR2003211
37	P Seidel, More about vanishing cycles and mutation, from: "Symplectic geometry and mirror symmetry (Seoul, 2000)" (editors K Fukaya, Y G Oh, K Ono, G Tian), World Sci. Publ. (2001) 429 MR1882336
38	P Seidel, Vanishing cycles and mutation, from: "European Congress of Mathematics, Vol. II (Barcelona, 2000)" (editors C Casacuberta, R M Miró-Roig, J Verdera, S Xambó-Descamps), Progr. Math. 202, Birkhäuser (2001) 65 MR1905352
39	P Seidel, A long exact sequence for symplectic Floer cohomology, Topology 42 (2003) 1003 MR1978046
40	P Seidel, $A_\infty$–subalgebras and natural transformations, Homology, Homotopy Appl. 10 (2008) 83 MR2426130
41	P Seidel, Fukaya categories and Picard–Lefschetz theory, Zurich Lectures in Advanced Math., European Math. Soc. (2008) MR2441780
42	P Seidel, Symplectic homology as Hochschild homology, from: "Algebraic geometry—Seattle 2005. Part 1" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 415
43	P Seidel, Homological mirror symmetry for the genus two curve, J. Algebraic Geom. 20 (2011) 727 MR2819674
44	N Sheridan, On the homological mirror symmetry conjecture for pairs of pants and affine Fermat hypersurfaces arXiv:1012.3238
45	C Viterbo, Functors and computations in Floer homology with applications, I, Geom. Funct. Anal. 9 (1999) 985 MR1726235
46	A Weinstein, Contact surgery and symplectic handlebodies, Hokkaido Math. J. 20 (1991) 241 MR1114405
47	M L Yau, Cylindrical contact homology of subcritical Stein-fillable contact manifolds, Geom. Topol. 8 (2004) 1243 MR2087083