Geometry & Topology Volume 27, issue 8 (2023)

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Formal groups and quantum cohomology

Paul Seidel

Geometry & Topology 27 (2023) 2937–3060

DOI: 10.2140/gt.2023.27.2937

Bibliography

1	C Allday, V Puppe, Cohomological methods in transformation groups, 32, Cambridge Univ. Press (1993) MR1236839
2	G Alston, L Amorim, Floer cohomology of torus fibers and real Lagrangians in Fano toric manifolds, Int. Math. Res. Not. 2012 (2012) 2751 MR2942709
3	S Axelrod, I M Singer, Chern–Simons perturbation theory, II, J. Differential Geom. 39 (1994) 173 MR1258919
4	Y Bespalov, V Lyubashenko, O Manzyuk, Pretriangulated A_∞–categories, 76, NAS Ukraine, Institute of Math. (2008) 599 MR2513383
5	N Bottman, 2–associahedra, Algebr. Geom. Topol. 19 (2019) 743 MR3924177
6	N Bottman, Moduli spaces of witch curves topologically realize the 2–associahedra, J. Symplectic Geom. 17 (2019) 1649 MR4057724
7	N Bottman, S Carmeli, (A_∞,2)–categories and relative 2–operads, High. Struct. 5 (2021) 401 MR4367226
8	N Bottman, A Oblomkov, A compactification of the moduli space of marked vertical lines in ℂ², preprint (2019) arXiv:1910.02037
9	N Bottman, K Wehrheim, Gromov compactness for squiggly strip shrinking in pseudoholomorphic quilts, Selecta Math. 24 (2018) 3381 MR3848023
10	K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
11	T Coates, A Corti, S Galkin, V Golyshev, A Kasprzyk, Fano varieties and extremal Laurent polynomials, electronic reference (2012)
12	T Coates, A Corti, S Galkin, V Golyshev, A Kasprzyk, Mirror symmetry and Fano manifolds, from: "European Congress of Mathematics" (editors R Latała, A Ruciński, P Strzelecki, J Świątkowski, D Wrzosek, P Zakrzewski), Eur. Math. Soc. (2013) 285 MR3469127
13	T Coates, A Corti, S Galkin, A Kasprzyk, Quantum periods for 3–dimensional Fano manifolds, Geom. Topol. 20 (2016) 103 MR3470714
14	F R Cohen, The homology of C_n+1–spaces, n ≥ 0, from: "The homology of iterated loop spaces" (editors F R Cohen, T J Lada, J P May), Lecture Notes in Math. 533, Springer (1976) 207 MR0436146
15	S K Donaldson, Gluing techniques in the cohomology of moduli spaces, from: "Topological methods in modern mathematics" (editors L R Goldberg, A V Phillips), Publish or Perish (1993) 137 MR1215963
16	S K Donaldson, Floer homology and algebraic geometry, from: "Vector bundles in algebraic geometry" (editors N J Hitchin, P E Newstead, W M Oxbury), London Math. Soc. Lecture Note Ser. 208, Cambridge Univ. Press (1995) 119 MR1338415
17	G C Drummond-Cole, Homotopically trivializing the circle in the framed little disks, J. Topol. 7 (2014) 641 MR3252959
18	J D Evans, Y Lekili, Floer cohomology of the Chiang Lagrangian, Selecta Math. 21 (2015) 1361 MR3397452
19	J Fine, D Panov, Hyperbolic geometry and non-Kähler manifolds with trivial canonical bundle, Geom. Topol. 14 (2010) 1723 MR2679581
20	A Floer, H Hofer, D Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. J. 80 (1995) 251 MR1360618
21	K Fukaya, Morse homotopy and its quantization, from: "Geometric topology" (editor W H Kazez), AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 409 MR1470740
22	K Fukaya, Unobstructed immersed Lagrangian correspondence and filtered A_∞ functor, preprint (2017) arXiv:1706.02131
23	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory : anomaly and obstruction, I, 46.1, Amer. Math. Soc. (2009) MR2553465
24	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory : anomaly and obstruction, II, 46.2, Amer. Math. Soc. (2009) MR2548482
25	W Fulton, R MacPherson, A compactification of configuration spaces, Ann. of Math. 139 (1994) 183 MR1259368
26	S Ganatra, Symplectic cohomology and duality for the wrapped Fukaya category, preprint (2013) arXiv:1304.7312
27	M Gerstenhaber, A A Voronov, Homotopy G–algebras and moduli space operad, Int. Math. Res. Notices (1995) 141 MR1321701
28	E Getzler, Batalin–Vilkovisky algebras and two-dimensional topological field theories, Comm. Math. Phys. 159 (1994) 265 MR1256989
29	E Getzler, J D S Jones, Operads, homotopy algebra and iterated integrals for double loop spaces, preprint (1994) arXiv:hep-th/9403055
30	T Graber, R Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999) 487 MR1666787
31	J Harris, I Morrison, Moduli of curves, 187, Springer (1998) MR1631825
32	M Hazewinkel, Three lectures on formal groups, from: "Lie algebras and related topics" (editors D J Britten, F W Lemire, R V Moody), CMS Conf. Proc. 5, Amer. Math. Soc. (1986) 51 MR832194
33	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
34	T Honda, Formal groups and zeta-functions, Osaka Math. J. 5 (1968) 199 MR249438
35	K Hori, S Katz, A Klemm, R Pandharipande, R Thomas, C Vafa, R Vakil, E Zaslow, Mirror symmetry, 1, Amer. Math. Soc. (2003) MR2003030
36	D Joyce, A generalization of manifolds with corners, Adv. Math. 299 (2016) 760 MR3519481
37	T Kimura, J Stasheff, A A Voronov, On operad structures of moduli spaces and string theory, Comm. Math. Phys. 171 (1995) 1 MR1341693
38	M Kontsevich, Y Manin, Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994) 525 MR1291244
39	M Lazard, Commutative formal groups, 443, Springer (1975) MR0393050
40	Y Lekili, M Lipyanskiy, Geometric composition in quilted Floer theory, Adv. Math. 236 (2013) 1 MR3019714
41	Y Lekili, T Perutz, Arithmetic mirror symmetry for the 2–torus, preprint (2012) arXiv:1211.4632
42	Y Lekili, A Polishchuk, Arithmetic mirror symmetry for genus 1 curves with n marked points, Selecta Math. 23 (2017) 1851 MR3663596
43	T L collaboration, The L–functions and modular forms database, electronic reference (2019)
44	V Lyubashenko, Category of A_∞–categories, Homology Homotopy Appl. 5 (2003) 1 MR1989611
45	V Lyubashenko, O Manzyuk, Unital A_∞–categories, preprint (2008) arXiv:0802.2885
46	S MacLane, Homology, 114, Springer (1967) MR0349792
47	S Ma’u, Quilted strips, graph associahedra, and A_∞ n–modules, Algebr. Geom. Topol. 15 (2015) 783 MR3342676
48	S Ma’u, K Wehrheim, C Woodward, A_∞ functors for Lagrangian correspondences, Selecta Math. 24 (2018) 1913 MR3816496
49	S Ma’u, C Woodward, Geometric realizations of the multiplihedra, Compos. Math. 146 (2010) 1002 MR2660682
50	J P May, A general algebraic approach to Steenrod operations, from: "The Steenrod algebra and its applications" (editor F P Peterson), Lecture Notes in Math. 168, Springer (1970) 153 MR0281196
51	J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR0420610
52	J H McClellan, T W Parks, Eigenvalue and eigenvector decomposition of the discrete Fourier transform, IEEE Trans. Audio Electroacoust. AU-20 (1972) 66 MR0399751
53	J E McClure, J H Smith, A solution of Deligne’s Hochschild cohomology conjecture, from: "Recent progress in homotopy theory" (editors D M Davis, J Morava, G Nishida, W S Wilson, N Yagita), Contemp. Math. 293, Amer. Math. Soc. (2002) 153 MR1890736
54	D McDuff, D Salamon, J–holomorphic curves and quantum cohomology, 6, Amer. Math. Soc. (1994) MR1286255
55	J J Millson, On the first Betti number of a constant negatively curved manifold, Ann. of Math. 104 (1976) 235 MR422501
56	L D Olson, Hasse invariants and anomalous primes for elliptic curves with complex multiplication, J. Number Theory 8 (1976) 397 MR450191
57	R Pandharipande, Rational curves on hypersurfaces (after A. Givental), from: "Séminaire Bourbaki, Vol. 1997/98", Astérisque 252, Soc. Math. France (1998) 307 MR1685628
58	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
59	M Reid, The complete intersection of two or more quadrics, DPhil thesis, University of Cambridge (1972)
60	A G Reznikov, Symplectic twistor spaces, Ann. Global Anal. Geom. 11 (1993) 109 MR1225431
61	Y Ruan, G Tian, Bott-type symplectic Floer cohomology and its multiplication structures, Math. Res. Lett. 2 (1995) 203 MR1324703
62	P Salvatore, Configuration spaces with summable labels, from: "Cohomological methods in homotopy theory" (editors J Aguadé, C Broto, C Casacuberta), Progr. Math. 196, Birkhäuser (2001) 375 MR1851264
63	M Schlessinger, Functors of Artin rings, Trans. Amer. Math. Soc. 130 (1968) 208 MR217093
64	P Seidel, A_∞–subalgebras and natural transformations, Homology Homotopy Appl. 10 (2008) 83 MR2426130
65	P Seidel, Fukaya categories and Picard–Lefschetz theory, Eur. Math. Soc. (2008) MR2441780
66	P Seidel, N Wilkins, Covariant constancy of quantum Steenrod operations, J. Fixed Point Theory Appl. 24 (2022) 52 MR4440845
67	N Sheridan, On the Fukaya category of a Fano hypersurface in projective space, Publ. Math. Inst. Hautes Études Sci. 124 (2016) 165 MR3578916
68	D P Sinha, The (non-equivariant) homology of the little disks operad, from: "Operads 2009" (editors J L Loday, B Vallette), Sémin. Congr. 26, Soc. Math. France (2013) 253 MR3203375
69	I Smith, Floer cohomology and pencils of quadrics, Invent. Math. 189 (2012) 149 MR2929086
70	N E Steenrod, Cohomology operations, 50, Princeton Univ. Press (1962) MR0145525
71	V Tourtchine, Dyer–Lashof–Cohen operations in Hochschild cohomology, Algebr. Geom. Topol. 6 (2006) 875 MR2240919
72	A A Voronov, M Gerstenkhaber, Higher-order operations on the Hochschild complex, Funktsional. Anal. i Prilozhen. 29 (1995) 1 MR1328534
73	C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324
74	N Wilkins, A construction of the quantum Steenrod squares and their algebraic relations, Geom. Topol. 24 (2020) 885 MR4153653
75	N Wilkins, Quantum Steenrod squares and the equivariant pair-of-pants in symplectic cohomology, J. Topol. Anal. 15 (2023) 1 MR4548627
76	J Young, Brace bar–cobar duality, preprint (2013) arXiv:1309.2820
77	A Zimmermann, Fine Hochschild invariants of derived categories for symmetric algebras, J. Algebra 308 (2007) 350 MR2290926