Lagrangian Quantum Homology

The present paper is mainly a survey of our work arXiv:0708.4221 and arXiv:0808.2440 but it also contains the announcement of some new results. Its main purpose is to present an accessible introduction to a technique allowing efficient calculations in Lagrangian Floer theory.

[1]  Peter Albers.  A Lagrangian Piunikhin-Salamon-Schwarz Morphism and Two Comparison Homomorphisms in Floer Homology , 2005, math/0512037.

[2]  O. Cornea,et al.  Rigidity and uniruling for Lagrangian submanifolds , 2008, 0808.2440.

[3]  L. Polterovich,et al.  Rigid subsets of symplectic manifolds , 2007, Compositio Mathematica.

[4]  Y. Oh,et al.  Lagrangian intersection floer theory : anomaly and obstruction , 2009 .

[5]  Y. Oh,et al.  Lagrangian Floer theory on compact toric manifolds II: bulk deformations , 2008, 0802.1703.

[6]  O. Cornea,et al.  Quantum Structures for Lagrangian Submanifolds , 2007, 0708.4221.

[7]  Lev Buhovski.  Multiplicative structures in Lagrangian Floer homology , 2006 .

[8]  Lev Buhovsky.  Multiplicative Structures in Lagrangian Floer Homology , 2006 .

[9]  F. Lalonde,et al.  Cluster Homology , 2005, math/0508345.

[10]  Peter Albers.  On the extrinsic topology of Lagrangian submanifolds , 2005, math/0506016.

[11]  Cheol-hyun Cho,et al.  Products of Floer Cohomology of Torus Fibers in Toric Fano Manifolds , 2004, math/0412414.

[12]  Y. Oh.  Relative Floer and quantum cohomology and the symplectic topology of Lagrangian submanifolds , 2005 .

[13]  P. Biran.  Lagrangian non-intersections , 2004, math/0412110.

[14]  P. Biran.  SYMPLECTIC TOPOLOGY AND ALGEBRAIC FAMILIES , 2004 .

[15]  Dusa McDuff,et al.  J-Holomorphic Curves and Symplectic Topology , 2004 .

[16]  Cheol-hyun Cho,et al.  Holomorphic discs, spin structures, and Floer cohomology of the Clifford torus , 2003, math/0308224.

[17]  Y. Oh,et al.  Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds , 2003, math/0308225.

[18]  P. Biran.  Geometry of Symplectic Intersections , 2003, math/0304260.

[19]  P. Biran.  Lagrangian barriers and symplectic embeddings , 2001 .

[20]  L. Lazzarini.  Existence of a somewhere injective pseudo-holomorphic disc , 2000 .

[21]  D. Salamon,et al.  Loops of Lagrangian submanifolds and pseudoholomorphic discs , 2000, math/0003079.

[22]  O. Yong-Geun,et al.  Structure of the image of (pseudo)-holomorphic discs with totally real boundary condition , 2000 .

[23]  Paul Seidel,et al.  Graded Lagrangian submanifolds , 1999, math/9903049.

[24]  W. Kazez.  Morse homotopy and its quantization , 1996 .

[25]  Y. Oh.  Floer cohomology, spectral sequences, and the Maslov class of Lagrangian embeddings , 1996 .

[26]  D. Salamon,et al.  Symplectic Floer-Donaldson theory and quantum cohomology , 1996 .

[27]  Y. Oh.  Addendum to “Floer Cohomology of Lagrangian Intersections and Pseudo-Holomorphic Discs, I” , 1995 .

[28]  L. Polterovich,et al.  Symplectic rigidity: Lagrangian submanifolds , 1994 .

[29]  Yong-Geun Oh,et al.  Floer cohomology of lagrangian intersections and pseudo‐holomorphic disks I , 1993 .

[30]  M. Gromov.  Pseudo holomorphic curves in symplectic manifolds , 1985 .