Volume 21, issue 6 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 26
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
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
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 An, 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 –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 Dn, Algebra i Analiz 23 (2011) 99 MR2918425
72 Y V Volkov, A I Generalov, Hochschild cohomology for self-injective algebras of tree class Dn, 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