References
From Talbot
Books/Monographs
- Seidel, Fukaya Categories and Picard-Lefschetz Theory. Sold at the AMS store.
- Fukaya, Oh, Ohta, and Ono, Lagrangian Floer Theory: Anomaly and Obstruction. Not available online, but see Fukaya's webpage for the earlier 2000 version (reference number 11 on Fukaya's page, link below)
Holomorphic Curves material: Not about Lagrangian floer homology, but potentially useful background information, and sets up the relevant analysis. A lot of the analysis/bubbling arguments are similar:
- Salamon's lecture notes on Floer Homology. The Hamiltonian Floer homology case, a good place to start. Contains an good, concise discussion of bubbling in this case.
- McDuff, Salamon, J-Holomorphic Curves and Symplectic Topology. Google Books Link. The earlier (much smaller) edition, J-Holomorphic curves and Quantum Cohomology is available online but doesn't use the language of stable maps.
Papers
A-infinity Structures
- Keller, Introduction to A-infinity Algebras and modules
- Merkulov, Strongly homotopy algebras of a Kähler manifold. Discusses a natural hodge-theoretic A-infinity algebra associated to a Kahler manifold which in part "explains" why the wedge of d^* closed forms is not in general d^* closed.
Examples
- Combinatorial examples: Abouzaid, On the Fukaya Categories of Higher Genus Surfaces. In this setting, the Fukaya Category can be described in terms of elementary/combinatorial objects.
- Fukaya, Oh, Ohta and Ono, Lagrangian Floer theory on compact toric manifolds (currently at 2 out of 5 expected parts).
- Cotangent bundles: Various papers about cotangent bundles: Nadler, Nadler-Zaslow and Fukaya Seidel-Smith. Seidel's <math>T^*S^n</math> paper has a reasonable exposition for beginners.
- Lefschetz Fibrations: Seidel's Vanishing Cycles and Mutation papers. Discusses the Fukaya-type category of vanishing cycles/thimbles associated to a Lefschetz fibration. Another account of this as well as general background on Lefschetz fibrations can be found in the lecture notes of Auroux's 2003 IPAM talks. See also Seidel's book.
Homological Mirror Symmetry
- Kontsevich, Homological Algebra of Mirror Symmetry. The original paper announcing the HMS conjecture.
- Kontsevich and Soibelman, Homological Mirror Symmetry and Torus Fibrations
- Polishchuk and Zaslow's Elliptic Curve example
- papers of Auroux, Katzarkov, Orlov on HMS for Del Pezzo Surfaces and weighted projective planes
- Seidel, Homological Mirror Symmetry for the quartic surface. Homological Mirror Symmetry for the genus two curve
Misc.
- Wehrheim and Woodward, Functoriality for Lagrangian correspondences in Floer theory. Discussion of the symplectic 2-category and the pseudo-holomorphic quilts formalism.
