Volume 19, issue 2 (2015)

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Bimodules in bordered Heegaard Floer homology

Robert Lipshitz, Peter S Ozsváth and Dylan P Thurston

Geometry & Topology 19 (2015) 525–724
Bibliography
1 J E Andersen, A J Bene, R C Penner, Groupoid extensions of mapping class representations for bordered surfaces, Topology Appl. 156 (2009) 2713 MR2556030
2 J C Baez, A D Lauda, Higher-dimensional algebra, V: $2$–groups, Theory Appl. Categ. 12 (2004) 423 MR2068521
3 J Bénabou, Introduction to bicategories, from: "Reports of the Midwest Category Seminar", Springer (1967) 1 MR0220789
4 A J Bene, A chord diagrammatic presentation of the mapping class group of a once bordered surface, Geom. Dedicata 144 (2010) 171 MR2580425
5 J Bernstein, V Lunts, Equivariant sheaves and functors, Lecture Notes in Math. 1578, Springer (1994) MR1299527
6 A Björner, M Wachs, Bruhat order of Coxeter groups and shellability, Adv. in Math. 43 (1982) 87 MR644668
7 A I Bondal, M M Kapranov, Framed triangulated categories, Mat. Sb. 181 (1990) 669 MR1055981
8 J B Etnyre, Lectures on open book decompositions and contact structures, from: "Floer homology, gauge theory and low-dimensional topology" (editors D A Ellwood, P S Ozsváth, A I Stipsicz, Z Szabó), Clay Math. Proc. 5, Amer. Math. Soc. (2006) 103 MR2249250
9 N Ganter, M Kapranov, Representation and character theory in $2$–categories, Adv. Math. 217 (2008) 2268 MR2388094
10 H Geiges, An introduction to contact topology, Cambridge Studies in Adv. Math. 109, Cambridge Univ. Press (2008) MR2397738
11 B Keller, A brief introduction to $A$–infinity algebras
12 B Keller, Koszul duality and coderived categories (after K Lefévre)
13 B Keller, Introduction to $A$–infinity algebras and modules, Homology Homotopy Appl. 3 (2001) 1 MR1854636
14 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. (2006) 151 MR2275593
15 M Khovanov, Link homology and categorification, from: "International Congress of Mathematicians, Vol. II" (editors M Sanz-Solé, J Soria, J L Varona, J Verdera), Eur. Math. Soc. (2006) 989 MR2275632
16 M Khovanov, R Thomas, Braid cobordisms, triangulated categories, and flag varieties, Homology Homotopy Appl. 9 (2007) 19 MR2366943
17 M Kontsevich, Homological algebra of mirror symmetry, from: "Proceedings of the International Congress of Mathematicians, Vol. $1$, $2$" (editor S D Chatterji), Birkhäuser (1995) 120 MR1403918
18 M Kontsevich, Y Soibelman, Homological mirror symmetry and torus fibrations, from: "Symplectic geometry and mirror symmetry" (editors K Fukaya, Y G Oh, K Ono, G Tian), World Scientific (2001) 203 MR1882331
19 K Lefèvre-Hasegawa, Sur les $A_{\infty}$ catégories, PhD thesis, Université Denis Diderot (2003) arXiv:math.CT/0310337
20 R Lipshitz, P S Ozsváth, D P Thurston, Computing $\widehat{\mathit{HF}}$ by factoring mapping classes, arXiv:1010.2550
21 R Lipshitz, P S Ozsváth, D P Thurston, Bordered Heegaard Floer homology: Invariance and pairing, (2011) arXiv:0810.0687v4
22 R Lipshitz, P S Ozsváth, D P Thurston, Heegaard Floer homology as morphism spaces, Quantum Topol. 2 (2011) 381 MR2844535
23 R Lipshitz, P S Ozsváth, D P Thurston, A faithful linear-categorical action of the mapping class group of a surface with boundary, J. Eur. Math. Soc. $($JEMS$)$ 15 (2013) 1279 MR3055762
24 J L Loday, The diagonal of the Stasheff polytope, from: "Higher structures in geometry and physics" (editors A S Cattaneo, A Giaquinto, P Xu), Progr. Math. 287, Springer (2011) 269 MR2762549
25 S Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer (1998) MR1712872
26 M Markl, S Shnider, Associahedra, cellular $W$–construction and products of $A_\infty$–algebras, Trans. Amer. Math. Soc. 358 (2006) 2353 MR2204035
27 C Năstăsescu, F Van Oystaeyen, Methods of graded rings, Lecture Notes in Math. 1836, Springer (2004) MR2046303
28 P S Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math 186 (2004) 58 arXiv:math.GT/0209056
29 P S Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. 159 (2004) 1027 MR2113019
30 P S Ozsváth, Z Szabó, Holomorphic triangles and invariants for smooth four-manifolds, Adv. Math. 202 (2006) 326 MR2222356
31 R C Penner, The decorated Teichmüller space of punctured surfaces, Comm. Math. Phys. 113 (1987) 299 MR919235
32 S B Priddy, Koszul resolutions, Trans. AMS 152 (1970) 39 MR0265437
33 S Saneblidze, R Umble, Diagonals on the permutahedra, multiplihedra and associahedra, Homology Homotopy Appl. 6 (2004) 363 MR2118493
34 P Seidel, Graded Lagrangian submanifolds, Bull. Soc. Math. France 128 (2000) 103 MR1765826
35 P Seidel, Fukaya categories and deformations, from: "Proceedings of the International Congress of Mathematicians, Vol. II" (editor T Li), Higher Ed. Press (2002) 351 MR1957046
36 P Seidel, Fukaya categories and Picard–Lefschetz theory, Zurich Lectures in Advanced Math., Eur. Math. Soc. (2008) MR2441780