Volume 16, issue 4 (2012)

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

Volume 29, 1 issue

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

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 Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Lagrangian homology spheres in $(A_{m})$ Milnor fibres via $\mathbb{C}^{*}$–equivariant $A_{\infty}$–modules

Paul Seidel

Geometry & Topology 16 (2012) 2343–2389
Bibliography
1 M Abouzaid, A geometric criterion for generating the Fukaya category, Publ. Math. Inst. Hautes Études Sci. (2010) 191 MR2737980
2 M Abouzaid, I Smith, Exact Lagrangians in plumbings arXiv:1107.0129
3 V I Arnold, V V Goryunov, O V Lyashko, V A Vasil’ev, Singularity theory. I, Springer (1998) MR1660090
4 A A Beĭlinson, J Bernstein, P Deligne, Faisceaux pervers, from: "Analysis and topology on singular spaces, I", Astérisque 100, Soc. Math. France (1982) 5 MR751966
5 J Bernstein, Algebraic theory of $D$–modules, unpublished lecture notes
6 R Bezrukavnikov, Perverse coherent sheaves (after Deligne) arXiv:math/0005152
7 R Bezrukavnikov, M Finkelberg, V Ginzburg, Cherednik algebras and Hilbert schemes in characteristic $p$ arXiv:math/0312474
8 A Bondal, M van den Bergh, Generators and representability of functors in commutative and noncommutative geometry, Mosc. Math. J. 3 (2003) 1, 258 MR1996800
9 A I Bondal, M M Kapranov, Homogeneous bundles, from: "Helices and vector bundles", London Math. Soc. Lecture Note Ser. 148, Cambridge Univ. Press (1990) 45 MR1074782
10 A Căldăraru, S Willerton, The Mukai pairing. I. A categorical approach, New York J. Math. 16 (2010) 61 MR2657369
11 A Dold, Zur Homotopietheorie der Kettenkomplexe, Math. Ann. 140 (1960) 278 MR0112906
12 V Drinfeld, DG quotients of DG categories, J. Algebra 272 (2004) 643 MR2028075
13 J D Evans, Symplectic mapping class groups of some Stein and rational surfaces, J. Symplectic Geom. 9 (2011) 45 MR2787361
14 G Hochschild, Cohomology of algebraic linear groups, Illinois J. Math. 5 (1961) 492 MR0130901
15 M a Inaba, Toward a definition of moduli of complexes of coherent sheaves on a projective scheme, J. Math. Kyoto Univ. 42 (2002) 317 MR1966840
16 A Ishii, K Ueda, H Uehara, Stability conditions on $A_n$–singularities, J. Differential Geom. 84 (2010) 87 MR2629510
17 A Ishii, H Uehara, Autoequivalences of derived categories on the minimal resolutions of $A_n$–singularities on surfaces, J. Differential Geom. 71 (2005) 385 MR2198807
18 B Keller, Invariance and localization for cyclic homology of DG algebras, J. Pure Appl. Algebra 123 (1998) 223 MR1492902
19 B Keller, On the cyclic homology of exact categories, J. Pure Appl. Algebra 136 (1999) 1 MR1667558
20 B Keller, Bimodule complexes via strong homotopy actions, Algebr. Represent. Theory 3 (2000) 357 MR1808132
21 B Keller, Introduction to $A$–infinity algebras and modules, Homology Homotopy Appl. 3 (2001) 1 MR1854636
22 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
23 B Keller, On differential graded categories, from: "International Congress of Mathematicians. Vol. II" (editors M Sanz-Solé, J Soria, J L Varona, J Verdera), Eur. Math. Soc., Zürich (2006) 151 MR2275593
24 M Khovanov, P Seidel, Quivers, Floer cohomology, and braid group actions, J. Amer. Math. Soc. 15 (2002) 203 MR1862802
25 M Kontsevich, Homological algebra of mirror symmetry, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994)" (editor S D Chatterji), Birkhäuser (1995) 120 MR1403918
26 M Kontsevich, Y Soibelman, Notes on $A_\infty$–algebras, $A_\infty$–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
27 K Lefèvre-Hasegawa, Sur les $A_\infty$–catégories, PhD thesis, Université Paris 7 (2002) arXiv:math/0310337
28 Y Lekili, M Maydanskiy, The symplectic topology of some rational homology balls arXiv:1202.5625
29 Y Lekili, T Perutz, Fukaya categories of the torus and Dehn surgery, Proc. Natl. Acad. Sci. USA 108 (2011) 8106 MR2806646
30 M Lieblich, Moduli of complexes on a proper morphism, J. Algebraic Geom. 15 (2006) 175 MR2177199
31 J L Loday, Cyclic homology, Grundl. Math. Wissen. 301, Springer (1992) MR1217970
32 W Lück, A Ranicki, Chain homotopy projections, J. Algebra 120 (1989) 361 MR989903
33 J Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies 61, Princeton Univ. Press (1968) MR0239612
34 W Müller, The asymptotics of the Ray–Singer analytic torsion of hyperbolic $3$–manifolds arXiv:1003.5168
35 A Polishchuk, $K$–theoretic exceptional collections at roots of unity, J. K-Theory 7 (2011) 169 MR2774162
36 A F Ritter, Deformations of symplectic cohomology and exact Lagrangians in ALE spaces, Geom. Funct. Anal. 20 (2010) 779 MR2720232
37 R Rouquier, A Zimmermann, Picard groups for derived module categories, Proc. London Math. Soc. 87 (2003) 197 MR1978574
38 P Seidel, Abstract analogues of flux as symplectic invariants arXiv:1108.0394
39 P Seidel, Lagrangian two-spheres can be symplectically knotted, J. Differential Geom. 52 (1999) 145 MR1743463
40 P Seidel, A long exact sequence for symplectic Floer cohomology, Topology 42 (2003) 1003 MR1978046
41 P Seidel, Exact Lagrangian submanifolds in $T^{*}S^n$ and the graded Kronecker quiver, from: "Different faces of geometry" (editors S Donaldson, Y Eliashberg, M Gromov), Int. Math. Ser. (N. Y.) 3, Kluwer/Plenum (2004) 349 MR2103000
42 P Seidel, $A_\infty$–subalgebras and natural transformations, Homology, Homotopy Appl. 10 (2008) 83 MR2426130
43 P Seidel, Fukaya categories and Picard–Lefschetz theory, Zurich Lect. in Adv. Math. 8, Europ. Math. Soc. (2008) MR2441780
44 P Seidel, Suspending Lefschetz fibrations, with an application to local mirror symmetry, Comm. Math. Phys. 297 (2010) 515 MR2651908
45 P Seidel, I Smith, Localization for involutions in Floer cohomology, Geom. Funct. Anal. 20 (2010) 1464 MR2739000
46 P Seidel, J P Solomon, Symplectic cohomology and $q$–intersection numbers, Geom. Funct. Anal. 22 (2012) 443 MR2929070
47 P Seidel, R Thomas, Braid group actions on derived categories of coherent sheaves, Duke Math. J. 108 (2001) 37 MR1831820
48 D Shklyarov, Hirzebruch–Riemann–Roch theorem for DG algebras arXiv:0710.1937
49 B Toën, M Vaquié, Moduli of objects in dg–categories, Ann. Sci. École Norm. Sup. 40 (2007) 387 MR2493386