Volume 13, issue 5 (2009)

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

Volume 27
Issue 8, 2937–3385
Issue 7, 2497–2936
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415

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 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
Symplectic Floer homology of area-preserving surface diffeomorphisms

Andrew Cotton-Clay

Geometry & Topology 13 (2009) 2619–2674
Bibliography
1 M Bestvina, M Handel, Train-tracks for surface homeomorphisms, Topology 34 (1995) 109 MR1308491
2 J S Birman, M E Kidwell, Fixed points of pseudo-Anosov diffeomorphisms of surfaces, Adv. in Math. 46 (1982) 217 MR679909
3 F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder, Compactness results in symplectic field theory, Geom. Topol. 7 (2003) 799 MR2026549
4 A J Casson, S A Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Math. Soc. Student Texts 9, Cambridge Univ. Press (1988) MR964685
5 K Cieliebak, K Mohnke, Compactness for punctured holomorphic curves, J. Symplectic Geom. 3 (2005) 589 MR2235856
6 V Colin, K Honda, Reeb vector fields and open book decompositions arXiv:0809.5088
7 A Cotton-Clay, A sharp bound on fixed points of area-preserving surface diffeomorphisms, in preparation
8 S Dostoglou, D A Salamon, Self-dual instantons and holomorphic curves, Ann. of Math. $(2)$ 139 (1994) 581 MR1283871
9 E Eftekhary, Floer homology of certain pseudo-Anosov maps, J. Symplectic Geom. 2 (2004) 357 MR2131640
10 Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, GAFA 2000 (Tel Aviv, 1999), Geom. Funct. Anal. (2000) 560 MR1826267
11 O Fabert, Contact homology of Hamiltonian mapping tori arXiv:math/0609406v3
12 A Fathi, F Laudenbach, V Poenaru, editors, Travaux de Thurston sur les surfaces, Astérisque 66, Soc. Math. France (1991) 286 MR568308
13 A L Fel′shtyn, Floer homology, Nielsen theory, and symplectic zeta functions, Tr. Mat. Inst. Steklova 246 (2004) 283 MR2101299
14 A Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988) 513 MR965228
15 A Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989) 575 MR987770
16 A Floer, H Hofer, D Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. J. 80 (1995) 251 MR1360618
17 R Gautschi, Floer homology of algebraically finite mapping classes, J. Symplectic Geom. 1 (2003) 715 MR2039162
18 M Hutchings, An index inequality for embedded pseudoholomorphic curves in symplectizations, J. Eur. Math. Soc. $($JEMS$)$ 4 (2002) 313 MR1941088
19 M Hutchings, Reidemeister torsion in generalized Morse theory, Forum Math. 14 (2002) 209 MR1880912
20 M Hutchings, Floer homology of families. I, Algebr. Geom. Topol. 8 (2008) 435 MR2443235
21 M Hutchings, M Sullivan, The periodic Floer homology of a Dehn twist, Algebr. Geom. Topol. 5 (2005) 301 MR2135555
22 M Hutchings, M Sullivan, Rounding corners of polygons and the embedded contact homology of $T^3$, Geom. Topol. 10 (2006) 169 MR2207793
23 S Jabuka, T Mark, Heegaard Floer homology of certain mapping tori, Algebr. Geom. Topol. 4 (2004) 685 MR2100677
24 B J Jiang, J H Guo, Fixed points of surface diffeomorphisms, Pacific J. Math. 160 (1993) 67 MR1227504
25 P Kronheimer, T Mrowka, Monopoles and three-manifolds, New Math. Monogr. 10, Cambridge Univ. Press (2007) MR2388043
26 E Lebow, Embedded contact homology of $2$–torus bundles over the circle, PhD thesis, University of California, Berkeley (2007)
27 Y J Lee, Heegaard splittings and Seiberg–Witten monopoles, from: "Geometry and topology of manifolds" (editors U Boden Hans, I Hambleton, A J Nicas, B D Park), Fields Inst. Commun. 47, Amer. Math. Soc. (2005) 173 MR2189932
28 Y J Lee, Reidemeister torsion in Floer–Novikov theory and counting pseudo-holomorphic tori. I, J. Symplectic Geom. 3 (2005) 221 MR2199540
29 Y J Lee, Reidemeister torsion in Floer–Novikov theory and counting pseudo-holomorphic tori. II, J. Symplectic Geom. 3 (2005) 385 MR2198782
30 Y J Lee, C H Taubes, Periodic Floer homology and Seiberg–Witten Floer cohomology arXiv:0906.0383
31 G Liu, G Tian, On the equivalence of multiplicative structures in Floer homology and quantum homology, Acta Math. Sin. $($Engl. Ser.$)$ 15 (1999) 53 MR1701133
32 D McDuff, D Salamon, Introduction to symplectic topology, Oxford Math. Monogr., The Clarendon Press, Oxford Univ. Press (1998) MR1698616
33 L Mosher, Train track expansions of measured foliations, Preprint (2003)
34 P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. $(2)$ 159 (2004) 1027 MR2113019
35 R C Penner, A construction of pseudo-Anosov homeomorphisms, Trans. Amer. Math. Soc. 310 (1988) 179 MR930079
36 R C Penner, J L Harer, Combinatorics of train tracks, Annals of Math. Studies 125, Princeton Univ. Press (1992) MR1144770
37 T Perutz, A hypercube for fixed-point Floer homology, Lecture (2008)
38 T Perutz, Lagrangian matching invariants for fibred four-manifolds. II, Geom. Topol. 12 (2008) 1461 MR2421133
39 M Pozniak, Floer homology, Novikov rings and clean intersections, PhD thesis, University of Warwick (1994)
40 J Robbin, D Salamon, The spectral flow and the Maslov index, Bull. London Math. Soc. 27 (1995) 1 MR1331677
41 D Salamon, E Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math. 45 (1992) 1303 MR1181727
42 M Schwarz, Cohomology operations from $S^1$–cobordisms in Floer homology, PhD thesis, ETH Zürich (1995)
43 P Seidel, The symplectic Floer homology of a Dehn twist, Math. Res. Lett. 3 (1996) 829 MR1426539
44 P Seidel, More about vanishing cycles and mutation, from: "Symplectic geometry and mirror symmetry (Seoul, 2000)" (editors K Fukaya, Y G Oh, K Ono, G Tian), World Sci. Publ. (2001) 429 MR1882336
45 P Seidel, Symplectic Floer homology and the mapping class group, Pacific J. Math. 206 (2002) 219 MR1924827
46 C H Taubes, Seiberg Witten and Gromov invariants for symplectic $4$–manifolds, (R Wentworth, editor), First Intl. Press Lecture Ser. 2, Intl. Press (2000) MR1798809
47 C H Taubes, The Seiberg–Witten equations and the Weinstein conjecture, Geom. Topol. 11 (2007) 2117 MR2350473
48 C H Taubes, Embedded contact homology and Seiberg–Witten Floer cohomology I–IV, Preprint (2008)
49 W P Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. $($N.S.$)$ 19 (1988) 417 MR956596
50 M Usher, Vortices and a TQFT for Lefschetz fibrations on $4$–manifolds, Algebr. Geom. Topol. 6 (2006) 1677 MR2263047
51 M L Yau, A holomorphic $0$–surgery model for open books, Int. Math. Res. Not. (2007) MR2346631