Frontiers of Mathematics in China >
Analysis and geometry of Floer theory of Landau-Ginzburg model on ℂn
Received date: 04 Nov 2014
Accepted date: 08 Jul 2015
Published date: 18 Oct 2016
Copyright
This article studies the Floer theory of Landau-Ginzburg (LG) model on ℂn: We perturb the Kähler form within a xed Kähler class to guarantee the transversal intersection of Lefschetz thimbles. The C0 estimate for solutions of the LG Floer equation can be derived then by our analysis tools. The Fredholm property is guaranteed by all these results.
Key words： Symplectic geometry; Floer theory; Landau-Ginzburg (LG) model
Wenfeng JIANG . Analysis and geometry of Floer theory of Landau-Ginzburg model on ℂn[J]. Frontiers of Mathematics in China, 2016 , 11(6) : 1569 -1602 . DOI: 10.1007/s11464-016-0502-6
| 1 |
Fan H, Jarvis T, Ruan Y. The Witten equation and its virtual fundamental cycle. 2007, arXiv: 0712–4025
|
| 2 |
Fan H, Jarvis T, Ruan Y. Geometry and analysis of spin equations. Comm Pure Appl Math, 2008, 61: 715–788
|
| 3 |
Fan H, Jarvis T, Ruan Y. The Witten equation, mirror symmetry and quantum singularity theory. Ann Math, 2013, 178: 1–106
|
| 4 |
Fan H, Jiang W. Floer Theory of Landau-Ginzburg model on Kähler manifolds (in preparation)
|
| 5 |
Floer A. A relative Morse index for the symplectic action. Comm Pure Appl Math, 1988, 41(4): 393–407
|
| 6 |
Floer A. The unregularized gradient ow of the symplectic action. Comm Pure Appl Math, 1988, 41(6): 775–813
|
| 7 |
Floer A. Morse theory for Lagrangian intersections. J Differential Geom, 1988, 28(3): 513–547
|
| 8 |
Fukaya K, Oh Y G, Ohta H, Ono K. Lagrangian Floer theory on compact toric manifolds I. 2008, arXiv: 0802–1703
|
| 9 |
Fukaya K, Oh Y G, Ohta H, Ono K. Lagrangian Interesection Floer Theory: Anomaly and Obstruction. AMS/IP Studies in Advanced Mathematics, Vol 46. Providence /Somerville: Amer Math Soc/International Press, 2010
|
| 10 |
Gaiotto D, Moore G, Witten E. Algebra of the infrared: string eld theoretic structures in massive N = (2; 2) eld theory in two dimensions. arXiv: 1506–04087
|
| 11 |
Haydys A. Fukaya-Seidel category and gauge theory. 2010, arXiv: 1010–2353
|
| 12 |
Hori K, Iqbal A, Vafa C. D-branes and mirror symmetry. 2000, arXiv: hep-th/0005247
|
| 13 |
Kapranov M, Kontsevich M, Soibelman Y. Algebra of the infrared and secondary polytopes. 2014, arXiv: 1408–2673
|
| 14 |
Kapustin A, Li Y. D-branes in Landau-Ginzburg models and algebraic geometry. J High Energy Phys, 2003, (12): 005
|
| 15 |
Kontsevich M. Homological algebra of mirror symmetry. 1994, arXiv: alg-geom /9411018
|
| 16 |
McDuff D, Salamon D. J-Holomorphic Curves and Symplectic Topology. Amer Math Soc Colloquium Publications, Vol 52. Providence: Amer Math Soc, 2004
|
| 17 |
Oh Y G. Symplectic Topology and Floer Homology.http://www.math.wisc.edu/~oh/all.pdf
|
| 18 |
Orlov D. Triangulated categories of singularities and D-branes in Landau-Ginzburg models. 2003, arXiv: math/0302304
|
| 19 |
Orlov D. Matrix factorizations for nonaffine LG-models. Math Ann, 2012, 353(1): 95–108
|
| 20 |
Perko L. Differential Equations and Dynamical Systems. 3rd ed. Berlin: Springer, 2006
|
| 21 |
Robbin J, Salamon D. The spectral ow and the Maslov index. Bull Lond Math Soc, 1995, 27(1): 1–33
|
| 22 |
Ruan Y. Lefschetz thimbles and LG-Floer theory. Personal Communication, 2013
|
| 23 |
Seidel P. More about vanishing cycles and mutation. 2000, arXiv: math/0010032.
|
| 24 |
Seidel P. Vanishing cycles and mutation. In: European Congress of Mathematics. Basel: Birkhäuser, 2001, 65–85
|
| 25 |
Seidel P. Fukaya Categories and Picard-Lefschetz Theory.Zürich: European Math Soc, 2008
|
| 26 |
Seidel P. Fukaya A∞-structures associated to Lefschetz brations. I. J Symplectic Geom, 2012, 10(3): 325–388
|
| 27 |
Seidel P. Fukaya A∞-structures associated to Lefschetz brations. II. 2014, arXiv: 1404–1352
|
| 28 |
Sheridan N. Homological mirror symmetry for Calabi-Yau hypersurfaces in projective space. 2011, arXiv: 1111–0632
|
/
| 〈 |
|
〉 |