An exact sequence for Legendrian links
Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 191-230
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We obtain an exact sequence of cyclic Legendrian homology for Legendrian links. We present some examples in 3 dimensions and higher. In higher dimensions we count holomorphic curves via Morse flow trees developed by Ekholm.

DOI : 10.2140/agt.2015.15.191
Classification : 53D42, 57R17
Keywords: Legendrian surgery, Contact homology, Legendrian submanifolds

Eslami Rad, Anahita  1

1 Département de Mathématiques, Université Libre de Bruxelles, CP 218 Boulevard du Triomphe, 1050 Bruxelles, Belgium
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Eslami Rad, Anahita. An exact sequence for Legendrian links. Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 191-230. doi: 10.2140/agt.2015.15.191

[1] F Bourgeois, Introduction to contact homology, notes from a summer school in Berder : Holomorphic curves and contact topology (2003)

[2] F Bourgeois, A survey of contact homology, 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) 45

[3] F Bourgeois, K Cieliebak, T Ekholm, A note on Reeb dynamics on the tight 3–sphere, J. Mod. Dyn. 1 (2007) 597

[4] F Bourgeois, T Ekholm, Y Eliashberg, Effect of Legendrian surgery, Geom. Topol. 16 (2012) 301

[5] F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder, Compactness results in symplectic field theory, Geom. Topol. 7 (2003) 799

[6] Y Chekanov, Differential algebra of Legendrian links, Invent. Math. 150 (2002) 441

[7] G Dimitroglou Rizell, Knotted Legendrian surfaces with few Reeb chords, Algebr. Geom. Topol. 11 (2011) 2903

[8] T Ekholm, Morse flow trees and Legendrian contact homology in 1–jet spaces, Geom. Topol. 11 (2007) 1083

[9] T Ekholm, J Etnyre, M Sullivan, The contact homology of Legendrian submanifolds in R2n+1, J. Differential Geom. 71 (2005) 177

[10] T Ekholm, J Etnyre, M Sullivan, Nonisotopic Legendrian submanifolds in R2n+1, J. Differential Geom. 71 (2005) 85

[11] T Ekholm, J Etnyre, M Sullivan, Orientations in Legendrian contact homology and exact Lagrangian immersions, Internat. J. Math. 16 (2005) 453

[12] Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, Geom. Funct. Anal. (2000) 560

[13] J B Etnyre, L L Ng, J M Sabloff, Invariants of Legendrian knots and coherent orientations, J. Symplectic Geom. 1 (2002) 321

[14] H Geiges, An introduction to contact topology, 109, Cambridge Univ. Press (2008)

[15] K Honda, On the classification of tight contact structures, I, Geom. Topol. 4 (2000) 309

[16] D Mcduff, D Salamon, J–holomorphic curves and symplectic topology, 52, Amer. Math. Soc. (2004)

[17] L L Ng, Computable Legendrian invariants, Topology 42 (2003) 55

[18] J Robbin, D Salamon, The Maslov index for paths, Topology 32 (1993) 827

[19] P Seidel, A long exact sequence for symplectic Floer cohomology, Topology 42 (2003) 1003

[20] A Weinstein, Contact surgery and symplectic handlebodies, Hokkaido Math. J. 20 (1991) 241

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