#### Volume 13, issue 5 (2013)

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Obstructions to Lagrangian cobordisms between Legendrians via generating families

### Joshua M Sabloff and Lisa Traynor

Algebraic & Geometric Topology 13 (2013) 2733–2797
##### 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, An open string analogue of Viterbo functoriality, Geom. Topol. 14 (2010) 627 MR2602848 3 V I Arnol’d, Lagrange and Legendre cobordisms, I, Funktsional. Anal. i Prilozhen. 14 (1980) 1, 96 MR583797 4 V I Arnol’d, Lagrange and Legendre cobordisms, II, Funktsional. Anal. i Prilozhen. 14 (1980) 8, 95 MR595724 5 A Banyaga, D E Hurtubise, A proof of the Morse–Bott lemma, Expo. Math. 22 (2004) 365 MR2075744 6 F Bourgeois, A Oancea, An exact sequence for contact- and symplectic homology, Invent. Math. 175 (2009) 611 MR2471597 7 F Bourgeois, J M Sabloff, L Traynor, Lagrangian cobordisms via generating families with applications to Legendrian geography and botany, in preparation 8 B Chantraine, Lagrangian concordance of Legendrian knots, Algebr. Geom. Topol. 10 (2010) 63 MR2580429 9 Y V Chekanov, Critical points of quasifunctions, and generating families of Legendrian manifolds, Funktsional. Anal. i Prilozhen. 30 (1996) 56, 96 MR1402081 10 W Chongchitmate, L Ng, An atlas of Legendrian knots, Exp. Math. 22 (2013) 26 MR3038780 11 G Civan, P Koprowski, J B Etnyre, J M Sabloff, A Walker, Product structures for Legendrian contact homology, Math. Proc. Cambridge Philos. Soc. 150 (2011) 291 MR2770065 12 P Eiseman, J D Lima, J M Sabloff, L Traynor, A partial ordering on slices of planar Lagrangians, J. Fixed Point Theory Appl. 3 (2008) 431 MR2434456 13 T Ekholm, Rational symplectic field theory over $\mathbb Z_2$ for exact Lagrangian cobordisms, J. Eur. Math. Soc. $($JEMS$)$ 10 (2008) 641 MR2421157 14 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 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 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 B Etnyre, M Sullivan, Non-isotopic Legendrian submanifolds in $\mathbb R^{2n+1}$, J. Differential Geom. 71 (2005) 85 MR2191769 18 T Ekholm, J B 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 arXiv:1212.1519 20 Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, Geom. Funct. Anal. (2000) 560 MR1826267 21 J B Etnyre, L Ng, V Vertesi, Legendrian and transverse twist knots, to apear in J. Eur. Math. Soc. 22 A Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988) 513 MR965228 23 D Fuchs, Chekanov–Eliashberg invariant of Legendrian knots: existence of augmentations, J. Geom. Phys. 47 (2003) 43 MR1985483 24 D Fuchs, T Ishkhanov, Invariants of Legendrian knots and decompositions of front diagrams, Mosc. Math. J. 4 (2004) 707, 783 MR2119145 25 D Fuchs, D Rutherford, Generating families and Legendrian contact homology in the standard contact space, J. Topol. 4 (2011) 190 MR2783382 26 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 27 R Golovko, A note on Lagrangian cobordisms between Legendrian submanifolds of $\mathbb{R}^{2n+1}$, Pacific J. Math. 261 (2013) 101 28 J E Grigsby, D Ruberman, S Strle, Knot concordance and Heegaard Floer homology invariants in branched covers, Geom. Topol. 12 (2008) 2249 MR2443966 29 M B Henry, Connections between Floer-type invariants and Morse-type invariants of Legendrian knots, Pacific J. Math. 249 (2011) 77 MR2764942 30 M B Henry, D Rutherford, A combinatorial DGA for Legendrian knots from generating families, Comm. Contemp. Math. 31 J Jordan, L Traynor, Generating family invariants for Legendrian links of unknots, Algebr. Geom. Topol. 6 (2006) 895 MR2240920 32 P B Kronheimer, T S Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Lett. 1 (1994) 797 MR1306022 33 P Melvin, S Shrestha, The nonuniqueness of Chekanov polynomials of Legendrian knots, Geom. Topol. 9 (2005) 1221 MR2174265 34 J Milnor, Morse theory, Annals of Math. Studies 51, Princeton Univ. Press (1963) MR0163331 35 P E Pushkar’, Y V Chekanov, Combinatorics of fronts of Legendrian links, and Arnol'd's 4-conjectures, Uspekhi Mat. Nauk 60 (2005) 99 MR2145660 36 G Rizell, Lifting pseudo-holomorphic polygons to the symplectisation of $P\times R$ and applications arXiv:1305.1572 37 J Robbin, D Salamon, The Maslov index for paths, Topology 32 (1993) 827 MR1241874 38 L Rudolph, An obstruction to sliceness via contact geometry and “classical” gauge theory, Invent. Math. 119 (1995) 155 MR1309974 39 J M Sabloff, Augmentations and rulings of Legendrian knots, Int. Math. Res. Not. 2005 (2005) 1157 MR2147057 40 J M Sabloff, Duality for Legendrian contact homology, Geom. Topol. 10 (2006) 2351 MR2284060 41 J M Sabloff, L Traynor, Obstructions to the existence and squeezing of Lagrangian cobordisms, J. Topol. Anal. 2 (2010) 203 MR2652907 42 S Sivek, A bordered Chekanov–Eliashberg algebra, J. Topol. 4 (2011) 73 MR2783378 43 S Sivek, Monopole Floer homology and Legendrian knots, Geom. Topol. 16 (2012) 751 MR2928982 44 E H Spanier, Algebraic topology, Springer (1981) MR666554 45 D Théret, A complete proof of Viterbo's uniqueness theorem on generating functions, Topology Appl. 96 (1999) 249 MR1709692 46 D Théret, A Lagrangian camel, Comment. Mathem. Helv. 74 (1999) 591 MR1730659 47 L Traynor, Generating function polynomials for Legendrian links, Geom. Topol. 5 (2001) 719 MR1871403 48 C Viterbo, Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992) 685 MR1157321