Geometry & Topology Volume 20, issue 4 (2016)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

Circle actions, quantum cohomology, and the Fukaya category of Fano toric varieties

Alexander F Ritter

Geometry & Topology 20 (2016) 1941–2052

DOI: 10.2140/gt.2016.20.1941

Bibliography

1	M Abouzaid, A geometric criterion for generating the Fukaya category, Publ. Math. Inst. Hautes Études Sci. 112 (2010) 191 MR2737980
2	P Albers, A Lagrangian Piunikhin–Salamon–Schwarz morphism and two comparison homomorphisms in Floer homology, Int. Math. Res. Not. 2008 (2008) MR2424172
3	D Auroux, Mirror symmetry and T–duality in the complement of an anticanonical divisor, J. Gökova Geom. Topol. GGT 1 (2007) 51 MR2386535
4	D Auroux, Special Lagrangian fibrations, wall-crossing, and mirror symmetry, from: "Geometry, analysis, and algebraic geometry : forty years of the Journal of Differential Geometry" (editors H D Cao, S T Yau), Surv. Differ. Geom. 13, Int. Press (2009) 1 MR2537081
5	V V Batyrev, Quantum cohomology rings of toric manifolds, from: "Journées de Géométrie Algébrique d’Orsay", Astérisque 218, Société Mathématique de France (1993) 9 MR1265307
6	V V Batyrev, On the classification of toric Fano 4–folds, J. Math. Sci. (New York) 94 (1999) 1021 MR1703904
7	P Biran, O Cornea, Rigidity and uniruling for Lagrangian submanifolds, Geom. Topol. 13 (2009) 2881 MR2546618
8	C H Cho, Products of Floer cohomology of torus fibers in toric Fano manifolds, Comm. Math. Phys. 260 (2005) 613 MR2183959
9	C H Cho, Non-displaceable Lagrangian submanifolds and Floer cohomology with non-unitary line bundle, J. Geom. Phys. 58 (2008) 1465 MR2463805
10	C H Cho, Y G Oh, Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds, Asian J. Math. 10 (2006) 773 MR2282365
11	K Cieliebak, D Salamon, Wall crossing for symplectic vortices and quantum cohomology, Math. Ann. 335 (2006) 133 MR2217687
12	D A Cox, S Katz, Mirror symmetry and algebraic geometry, 68, Amer. Math. Soc. (1999) MR1677117
13	T Dyckerhoff, Compact generators in categories of matrix factorizations, Duke Math. J. 159 (2011) 223 MR2824483
14	L C Evans, Partial differential equations, 19, Amer. Math. Soc. (1998) MR1625845
15	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory : anomaly and obstruction, I, II, 46, Amer. Math. Soc. (2009) MR2553465
16	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian Floer theory on compact toric manifolds, I, Duke Math. J. 151 (2010) 23 MR2573826
17	W Fulton, Introduction to toric varieties, 131, Princeton Univ. Press (1993) MR1234037
18	S Galkin, The conifold point, arXiv:1404.7388
19	S Ganatra, Symplectic cohomology and duality for the wrapped Fukaya category, PhD thesis, Massachusetts Institute of Technology (2012) MR3121862
20	A B Givental, Equivariant Gromov–Witten invariants, Int. Math. Res. Notices (1996) 613 MR1408320
21	A Givental, A mirror theorem for toric complete intersections, from: "Topological field theory, primitive forms and related topics" (editors M Kashiwara, A Matsuo, K Saito, I Satake), Progr. Math. 160, Birkhäuser (1998) 141 MR1653024
22	P Griffiths, J Harris, Principles of algebraic geometry, Wiley-Interscience (1978) MR507725
23	V Guillemin, Moment maps and combinatorial invariants of Hamiltonian Tⁿ–spaces, 122, Birkhäuser (1994) MR1301331
24	H Hofer, D A Salamon, Floer homology and Novikov rings, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 483 MR1362838
25	H Iritani, Convergence of quantum cohomology by quantum Lefschetz, J. Reine Angew. Math. 610 (2007) 29 MR2359850
26	T Kato, Perturbation theory for linear operators, 132, Springer (1980) MR0407617
27	J Kollár, Rational curves on algebraic varieties, 32, Springer (1996) MR1440180
28	Y P Lee, Quantum Lefschetz hyperplane theorem, Invent. Math. 145 (2001) 121 MR1839288
29	D McDuff, D Salamon, J–holomorphic curves and symplectic topology, 52, Amer. Math. Soc. (2004) MR2045629
30	D McDuff, S Tolman, Topological properties of Hamiltonian circle actions, Int. Math. Res. Pap. (2006) 1 MR2210662
31	D McDuff, S Tolman, Polytopes with mass linear functions, II : The four-dimensional case, Int. Math. Res. Not. 2013 (2013) 3509 MR3089735
32	Y Ostrover, I Tyomkin, On the quantum homology algebra of toric Fano manifolds, Selecta Math. 15 (2009) 121 MR2511201
33	A F Ritter, Novikov-symplectic cohomology and exact Lagrangian embeddings, Geom. Topol. 13 (2009) 943 MR2470967
34	A F Ritter, Topological quantum field theory structure on symplectic cohomology, J. Topol. 6 (2013) 391 MR3065181
35	A F Ritter, Floer theory for negative line bundles via Gromov–Witten invariants, Adv. Math. 262 (2014) 1035 MR3228449
36	A F Ritter, I Smith, The open-closed string map revisited, arXiv:1201.5880v1
37	A F Ritter, I Smith, The monotone wrapped Fukaya category and the open-closed string map, (2015) arXiv:1201.5880v4
38	P Seidel, π₁ of symplectic automorphism groups and invertibles in quantum homology rings, Geom. Funct. Anal. 7 (1997) 1046 MR1487754
39	P Seidel, Fukaya categories and deformations, from: "Proceedings of the International Congress of Mathematicians, II" (editor T Li), Higher Ed. Press (2002) 351 MR1957046
40	P Seidel, A biased view of symplectic cohomology, from: "Current developments in mathematics, 2006" (editors B Mazur, T Mrowka, W Schmid, R Stanley, S T Yau), Int. Press (2008) 211 MR2459307
41	C Viterbo, Functors and computations in Floer homology with applications, I, Geom. Funct. Anal. 9 (1999) 985 MR1726235