Geometry & Topology Volume 27, issue 9 (2023)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Cyclic homology, $S^1$–equivariant Floer cohomology and Calabi–Yau structures

Sheel Ganatra

Geometry & Topology 27 (2023) 3461–3584

DOI: 10.2140/gt.2023.27.3461

Bibliography

1	M Abouzaid, A geometric criterion for generating the Fukaya category, Publ. Math. Inst. Hautes Études Sci. 112 (2010) 191 MR2737980
2	M Abouzaid, K Fukaya, Y G Oh, H Ohta, K Ono, Quantum cohomology and split generation in Lagrangian Floer theory, in preparation
3	M Abouzaid, P Seidel, An open string analogue of Viterbo functoriality, Geom. Topol. 14 (2010) 627 MR2602848
4	P Albers, K Cieliebak, U Frauenfelder, Symplectic Tate homology, Proc. Lond. Math. Soc. 112 (2016) 169 MR3458149
5	F Bourgeois, T Ekholm, Y Eliashberg, Effect of Legendrian surgery, Geom. Topol. 16 (2012) 301 MR2916289
6	F Bourgeois, A Oancea, S¹–equivariant symplectic homology and linearized contact homology, Int. Math. Res. Not. 2017 (2017) 3849 MR3671507
7	C Brav, T Dyckerhoff, Relative Calabi–Yau structures, Compos. Math. 155 (2019) 372 MR3911626
8	D Burghelea, Cyclic homology and the algebraic K–theory of spaces, I, from: "Applications of algebraic K–theory to algebraic geometry and number theory, I, II" (editors S J Bloch, R K Dennis, E M Friedlander, M R Stein), Contemp. Math. 55, Amer. Math. Soc. (1986) 89 MR862632
9	C H Cho, S Lee, Potentials of homotopy cyclic A_∞–algebras, Homology Homotopy Appl. 14 (2012) 203 MR2954673
10	K Cieliebak, A Floer, H Hofer, Symplectic homology, II : A general construction, Math. Z. 218 (1995) 103 MR1312580
11	K Cieliebak, A Floer, H Hofer, K Wysocki, Applications of symplectic homology, II : Stability of the action spectrum, Math. Z. 223 (1996) 27 MR1408861
12	R Cohen, S Ganatra, Calabi–Yau categories, the Floer theory of the cotangent bundle, and the string topology of the base, in preparation
13	A Connes, Noncommutative differential geometry, Inst. Hautes Études Sci. Publ. Math. 62 (1985) 257 MR823176
14	K Costello, Topological conformal field theories and Calabi–Yau categories, Adv. Math. 210 (2007) 165 MR2298823
15	K Costello, The partition function of a topological field theory, J. Topol. 2 (2009) 779 MR2574744
16	V Dotsenko, S Shadrin, B Vallette, De Rham cohomology and homotopy Frobenius manifolds, J. Eur. Math. Soc. 17 (2015) 535 MR3323198
17	Y Félix, S Halperin, J C Thomas, Differential graded algebras in topology, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 829 MR1361901
18	A Floer, Witten’s complex and infinite-dimensional Morse theory, J. Differential Geom. 30 (1989) 207 MR1001276
19	A Floer, H Hofer, Symplectic homology, I : Open sets in ℂⁿ, Math. Z. 215 (1994) 37 MR1254813
20	K Fukaya, Cyclic symmetry and adic convergence in Lagrangian Floer theory, Kyoto J. Math. 50 (2010) 521 MR2723862
21	K Fukaya, Counting pseudo-holomorphic discs in Calabi–Yau 3–folds, Tohoku Math. J. 63 (2011) 697 MR2872962
22	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory : anomaly and obstruction, II, 46.2, Amer. Math. Soc. (2009) MR2553465
23	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian Floer theory and mirror symmetry on compact toric manifolds, 376, Soc. Math. France (2016) MR3460884
24	S Ganatra, Symplectic cohomology and duality for the wrapped Fukaya category, preprint (2013) arXiv:1304.7312
25	S Ganatra, Automatically generating Fukaya categories and computing quantum cohomology, preprint (2016) arXiv:1605.07702
26	S Ganatra, T Perutz, N Sheridan, The cyclic open–closed map and noncommutative Hodge structures, in preparation
27	S Ganatra, T Perutz, N Sheridan, Mirror symmetry: from categories to curve counts, preprint (2015) arXiv:1510.03839
28	V Ginzburg, Lectures on noncommutative geometry, lecture notes (2005) arXiv:math/0506603
29	D Kaledin, Non-commutative Hodge-to-de Rham degeneration via the method of Deligne–Illusie, Pure Appl. Math. Q. 4 (2008) 785 MR2435845
30	D Kaledin, Spectral sequences for cyclic homology, from: "Algebra, geometry, and physics in the 21st century" (editors D Auroux, L Katzarkov, T Pantev, Y Soibelman, Y Tschinkel), Progr. Math. 324, Birkhäuser (2017) 99 MR3702384
31	C Kassel, Cyclic homology, comodules, and mixed complexes, J. Algebra 107 (1987) 195 MR883882
32	B Keller, On the cyclic homology of exact categories, J. Pure Appl. Algebra 136 (1999) 1 MR1667558
33	B Keller, A–infinity algebras, modules and functor categories, from: "Trends in representation theory of algebras and related topics" (editors J A de la Peña, R Bautista), Contemp. Math. 406, Amer. Math. Soc. (2006) 67 MR2258042
34	T Kimura, J Stasheff, A A Voronov, On operad structures of moduli spaces and string theory, Comm. Math. Phys. 171 (1995) 1 MR1341693
35	M Kontsevich, XI Solomon Lefschetz memorial lecture series : Hodge structures in non-commutative geometry, from: "Non-commutative geometry in mathematics and physics" (editors G Dito, H García-Compeán, E Lupercio, F J Turrubiates), Contemp. Math. 462, Amer. Math. Soc. (2008) 1 MR2444365
36	M Kontsevich, Weak CY algebras, conference talk (2013)
37	M Kontsevich, Y Soibelman, Notes on A_∞–algebras, A_∞–categories and non-commutative geometry, from: "Homological mirror symmetry" (editors A Kapustin, M Kreuzer, K G Schlesinger), Lecture Notes in Phys. 757, Springer (2009) 153 MR2596638
38	M Kontsevich, A Takeda, Y Vlassopoulos, Pre-Calabi–Yau algebras and topological quantum field theories, preprint (2021) arXiv:2112.14667
39	M Kontsevich, A Takeda, Y Vlassopoulos, Smooth Calabi–Yau structures and the noncommutative Legendre transform, preprint (2023) arXiv:2301.01567
40	K Lefèvre-Hasegawa, Sur les A_∞ catégories, PhD thesis, Université Paris 7 – Denis Diderot (2003)
41	J L Loday, Cyclic homology, 301, Springer (1992) MR1217970
42	J L Loday, D Quillen, Cyclic homology and the Lie algebra homology of matrices, Comment. Math. Helv. 59 (1984) 569 MR780077
43	R McCarthy, The cyclic homology of an exact category, J. Pure Appl. Algebra 93 (1994) 251 MR1275967
44	J McCleary, A user’s guide to spectral sequences, 58, Cambridge Univ. Press (2001) MR1793722
45	L Menichi, String topology for spheres, Comment. Math. Helv. 84 (2009) 135 MR2466078
46	S Piunikhin, D Salamon, M Schwarz, Symplectic Floer–Donaldson theory and quantum cohomology, from: "Contact and symplectic geometry" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 171 MR1432464
47	A F Ritter, Topological quantum field theory structure on symplectic cohomology, J. Topol. 6 (2013) 391 MR3065181
48	P Seidel, Graded Lagrangian submanifolds, Bull. Soc. Math. France 128 (2000) 103 MR1765826
49	P Seidel, Fukaya categories and deformations, from: "Proceedings of the International Congress of Mathematicians, II" (editor T Li), Higher Ed. (2002) 351 MR1957046
50	P Seidel, A_∞–subalgebras and natural transformations, Homology Homotopy Appl. 10 (2008) 83 MR2426130
51	P Seidel, A biased view of symplectic cohomology, from: "Current developments in mathematics" (editors B Mazur, T Mrowka, W Schmid, R Stanley, S T Yau), International (2008) 211 MR2459307
52	P Seidel, Fukaya categories and Picard–Lefschetz theory, Eur. Math. Soc. (2008) MR2441780
53	P Seidel, Suspending Lefschetz fibrations, with an application to local mirror symmetry, Comm. Math. Phys. 297 (2010) 515 MR2651908
54	P Seidel, Categorical dynamics and symplectic topology, lecture notes (2013)
55	P Seidel, Disjoinable Lagrangian spheres and dilations, Invent. Math. 197 (2014) 299 MR3232008
56	P Seidel, Connections on equivariant Hamiltonian Floer cohomology, Comment. Math. Helv. 93 (2018) 587 MR3854903
57	P Seidel, Fukaya A_∞–structures associated to Lefschetz fibrations, VI, preprint (2018) arXiv:1810.07119
58	P Seidel, J P Solomon, Symplectic cohomology and q–intersection numbers, Geom. Funct. Anal. 22 (2012) 443 MR2929070
59	N Sheridan, Homological mirror symmetry for Calabi–Yau hypersurfaces in projective space, Invent. Math. 199 (2015) 1 MR3294958
60	N Sheridan, On the Fukaya category of a Fano hypersurface in projective space, Publ. Math. Inst. Hautes Études Sci. 124 (2016) 165 MR3578916
61	N Sheridan, Formulae in noncommutative Hodge theory, J. Homotopy Relat. Struct. 15 (2020) 249 MR4062886
62	T Tradler, Infinity-inner-products on A–infinity-algebras, J. Homotopy Relat. Struct. 3 (2008) 245 MR2426181
63	B L Tsygan, Homology of matrix Lie algebras over rings and the Hochschild homology, Uspekhi Mat. Nauk 38 (1983) 217 MR695483
64	C Viterbo, Functors and computations in Floer homology with applications, I, Geom. Funct. Anal. 9 (1999) 985 MR1726235
65	W K Yeung, Pre-Calabi–Yau structures and moduli of representations, preprint (2018) arXiv:1802.05398
66	J Zhao, Periodic symplectic cohomologies, J. Symplectic Geom. 17 (2019) 1513 MR4039816