Geometry & Topology Volume 21, issue 6 (2017)

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

Koszul duality patterns in Floer theory

Tolga Etgü and Yankı Lekili

Geometry & Topology 21 (2017) 3313–3389

DOI: 10.2140/gt.2017.21.3313

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, A cotangent fibre generates the Fukaya category, Adv. Math. 228 (2011) 894 MR2822213
3	M Abouzaid, A topological model for the Fukaya categories of plumbings, J. Differential Geom. 87 (2011) 1 MR2786590
4	M Abouzaid, On the wrapped Fukaya category and based loops, J. Symplectic Geom. 10 (2012) 27 MR2904032
5	M Abouzaid, Symplectic cohomology and Viterbo’s theorem, from: "Free loop spaces in geometry and topology" (editors J Latschev, A Oancea), IRMA Lect. Math. Theor. Phys. 24, Eur. Math. Soc. (2015) 271 MR3444367
6	M Abouzaid, P Seidel, An open string analogue of Viterbo functoriality, Geom. Topol. 14 (2010) 627 MR2602848
7	M Abouzaid, I Smith, Exact Lagrangians in plumbings, Geom. Funct. Anal. 22 (2012) 785 MR2984118
8	J F Adams, On the cobar construction, Proc. Nat. Acad. Sci. USA 42 (1956) 409 MR0079266
9	M J Bardzell, A C Locateli, E N Marcos, On the Hochschild cohomology of truncated cycle algebras, Comm. Algebra 28 (2000) 1615 MR1742678
10	A Beilinson, V Ginzburg, W Soergel, Koszul duality patterns in representation theory, J. Amer. Math. Soc. 9 (1996) 473 MR1322847
11	M van den Bergh, A relation between Hochschild homology and cohomology for Gorenstein rings, Proc. Amer. Math. Soc. 126 (1998) 1345 MR1443171
12	M Van den Bergh, Calabi–Yau algebras and superpotentials, Selecta Math. 21 (2015) 555 MR3338683
13	I N Bernšteĭn, I M Gel’fand, V A Ponomarev, Coxeter functors and Gabriel’s theorem, Uspekhi Mat. Nauk 28 (1973) 19 MR0393065
14	A J Blumberg, R L Cohen, C Teleman, Open-closed field theories, string topology, and Hochschild homology, from: "Alpine perspectives on algebraic topology" (editors C Ausoni, K Hess, J Scherer), Contemp. Math. 504, Amer. Math. Soc. (2009) 53 MR2581905
15	J M Boardman, Conditionally convergent spectral sequences, from: "Homotopy invariant algebraic structures" (editors J P Meyer, J Morava, W S Wilson), Contemp. Math. 239, Amer. Math. Soc. (1999) 49 MR1718076
16	F Bourgeois, T Ekholm, Y Eliashberg, Symplectic homology product via Legendrian surgery, Proc. Natl. Acad. Sci. USA 108 (2011) 8114 MR2806647
17	F Bourgeois, T Ekholm, Y Eliashberg, Effect of Legendrian surgery, Geom. Topol. 16 (2012) 301 MR2916289
18	S Brenner, M C R Butler, A D King, Periodic algebras which are almost Koszul, Algebr. Represent. Theory 5 (2002) 331 MR1930968
19	Y Chekanov, Differential algebra of Legendrian links, Invent. Math. 150 (2002) 441 MR1946550
20	R L Cohen, J D S Jones, A homotopy theoretic realization of string topology, Math. Ann. 324 (2002) 773 MR1942249
21	R L Cohen, J D S Jones, J Yan, The loop homology algebra of spheres and projective spaces, from: "Categorical decomposition techniques in algebraic topology" (editors G Arone, J Hubbuck, R Levi, M Weiss), Progr. Math. 215, Birkhäuser (2004) 77 MR2039760
22	P M Cohn, Free ideal rings and localization in general rings, 3, Cambridge Univ. Press (2006) MR2246388
23	W Crawley-Boevey, P Etingof, V Ginzburg, Noncommutative geometry and quiver algebras, Adv. Math. 209 (2007) 274 MR2294224
24	W Crawley-Boevey, P Shaw, Multiplicative preprojective algebras, middle convolution and the Deligne–Simpson problem, Adv. Math. 201 (2006) 180 MR2204754
25	P Deligne, P Griffiths, J Morgan, D Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math. 29 (1975) 245 MR0382702
26	G Dimitroglou Rizell, Nontriviality results for the characteristic algebra of a DGA, Math. Proc. Cambridge Philos. Soc. 162 (2017) 419 MR3628199
27	T Ekholm, Y Lekili, Duality between Lagrangian and Legendrian invariants, preprint (2017) arXiv:1701.01284
28	T Ekholm, L Ng, Legendrian contact homology in the boundary of a subcritical Weinstein 4–manifold, J. Differential Geom. 101 (2015) 67 MR3356070
29	Y Eliashberg, Topological characterization of Stein manifolds of dimension > 2, Internat. J. Math. 1 (1990) 29 MR1044658
30	Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, from: "Visions in mathematics: GAFA special volume" (editors N Alon, J Bourgain, A Connes, M Gromov, V Milman), Birkhäuser (2000) 560 MR1826267
31	Y Eliashberg, M Gromov, Convex symplectic manifolds, from: "Several complex variables and complex geometry, 2" (editors E Bedford, J P D’Angelo, R E Greene, S G Krantz), Proc. Sympos. Pure Math. 52, Amer. Math. Soc. (1991) 135 MR1128541
32	K Erdmann, T Holm, Twisted bimodules and Hochschild cohomology for self-injective algebras of class A_n, Forum Math. 11 (1999) 177 MR1680594
33	T Etgü, Y Lekili, Fukaya categories of plumbings and multiplicative preprojective algebras, preprint (2017) arXiv:1703.04515
34	P Etingof, V Ginzburg, Noncommutative complete intersections and matrix integrals, Pure Appl. Math. Q. 3 (2007) 107 MR2330156
35	P Etingof, V Ginzburg, Noncommutative del Pezzo surfaces and Calabi–Yau algebras, J. Eur. Math. Soc. 12 (2010) 1371 MR2734346
36	Y Félix, L Menichi, J C Thomas, Gerstenhaber duality in Hochschild cohomology, J. Pure Appl. Algebra 199 (2005) 43 MR2134291
37	H Geiges, An introduction to contact topology, 109, Cambridge Univ. Press (2008) MR2397738
38	M Gerstenhaber, C W Wilkerson, On the deformation of rings and algebras, V : Deformation of differential graded algebras, from: "Higher homotopy structures in topology and mathematical physics" (editor J McCleary), Contemp. Math. 227, Amer. Math. Soc. (1999) 89 MR1665463
39	V Ginzburg, Calabi–Yau algebras, unpublished manuscript (2006) arXiv:math.AG/0612139
40	R E Gompf, Handlebody construction of Stein surfaces, Ann. of Math. 148 (1998) 619 MR1668563
41	S Hermes, Minimal model of Ginzburg algebras, J. Algebra 459 (2016) 389 MR3503979
42	T Holm, Hochschild cohomology of Brauer tree algebras, Comm. Algebra 26 (1998) 3625 MR1647106
43	R S Huerfano, M Khovanov, A category for the adjoint representation, J. Algebra 246 (2001) 514 MR1872113
44	J D S Jones, J McCleary, Hochschild homology, cyclic homology, and the cobar construction, from: "Adams Memorial Symposium on Algebraic Topology, 1" (editors N Ray, G Walker), London Math. Soc. Lecture Note Ser. 175, Cambridge Univ. Press (1992) 53 MR1170570
45	T V Kadeishvili, The structure of the A(∞)–algebra, and the Hochschild and Harrison cohomologies, Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 91 (1988) 19 MR1029003
46	B Keller, Deriving DG categories, Ann. Sci. École Norm. Sup. 27 (1994) 63 MR1258406
47	B Keller, Derived invariance of higher structures on the Hochschild complex, unpublished manuscript (2003)
48	M Kwon, O van Koert, Brieskorn manifolds in contact topology, Bull. Lond. Math. Soc. 48 (2016) 173 MR3483060
49	Y Lekili, M Maydanskiy, The symplectic topology of some rational homology balls, Comment. Math. Helv. 89 (2014) 571 MR3260842
50	J L Loday, Cyclic homology, 301, Springer (1992) MR1217970
51	D M Lu, J H Palmieri, Q S Wu, J J Zhang, Koszul equivalences in A_∞–algebras, New York J. Math. 14 (2008) 325 MR2430869
52	R Martínez-Villa, Applications of Koszul algebras : the preprojective algebra, from: "Representation theory of algebras" (editors R Bautista, R Martínez-Villa, J A de la Peña), CMS Conf. Proc. 18, Amer. Math. Soc. (1996) 487 MR1388069
53	L Menichi, String topology for spheres, Comment. Math. Helv. 84 (2009) 135 MR2466078
54	S B Priddy, Koszul resolutions, Trans. Amer. Math. Soc. 152 (1970) 39 MR0265437
55	J Rickard, Derived categories and stable equivalence, J. Pure Appl. Algebra 61 (1989) 303 MR1027750
56	T Schedler, Zeroth Hochschild homology of preprojective algebras over the integers, v1, (2007) arXiv:0704.3278v1
57	T Schedler, Hochschild homology of preprojective algebras over the integers, Adv. Math. 299 (2016) 451 MR3519475
58	E Segal, The A_∞ deformation theory of a point and the derived categories of local Calabi–Yaus, J. Algebra 320 (2008) 3232 MR2450725
59	P Seidel, Graded Lagrangian submanifolds, Bull. Soc. Math. France 128 (2000) 103 MR1765826
60	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), Int. Press (2008) 211 MR2459307
61	P Seidel, Fukaya categories and Picard–Lefschetz theory, Eur. Math. Soc. (2008) MR2441780
62	P Seidel, Symplectic homology as Hochschild homology, from: "Algebraic geometry, 1" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math., Amer. Math. Soc. (2009) 415 MRMR2483942
63	P Seidel, Lectures on categorical dynamics and symplectic topology, (2013)
64	P Seidel, Abstract analogues of flux as symplectic invariants, 137, Soc. Math. Fr. (2014) 135 MR3289398
65	P Seidel, Fukaya A_∞–structures associated to Lefschetz fibrations, II1 /2, preprint (2015) arXiv:1504.06317
66	P Seidel, Picard–Lefschetz theory and dilating ℂ^∗–actions, J. Topol. 8 (2015) 1167 MR3431673
67	P Seidel, R Thomas, Braid group actions on derived categories of coherent sheaves, Duke Math. J. 108 (2001) 37 MR1831820
68	S F Siegel, S J Witherspoon, The Hochschild cohomology ring of a group algebra, Proc. London Math. Soc. 79 (1999) 131 MR1687539
69	I Smith, Quiver algebras as Fukaya categories, Geom. Topol. 19 (2015) 2557 MR3416110
70	C Viterbo, Functors and computations in Floer homology with applications, I, Geom. Funct. Anal. 9 (1999) 985 MR1726235
71	Y V Volkov, The Hochschild cohomology algebra for a series of self-injective algebras of tree type D_n, Algebra i Analiz 23 (2011) 99 MR2918425
72	Y V Volkov, A I Generalov, Hochschild cohomology for self-injective algebras of tree class D_n, I, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. 343 (2007) 121, 273 MR2469415
73	A Weinstein, Contact surgery and symplectic handlebodies, Hokkaido Math. J. 20 (1991) 241 MR1114405