Geometry & Topology Volume 15, issue 3 (2011)

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

Deformed Hamiltonian Floer theory, capacity estimates and Calabi quasimorphisms

Michael Usher

Geometry & Topology 15 (2011) 1313–1417

DOI: 10.2140/gt.2011.15.1313

Bibliography

1	A Banyaga, Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique, Comment. Math. Helv. 53 (1978) 174 MR490874
2	A Bayer, Semisimple quantum cohomology and blowups, Int. Math. Res. Not. (2004) 2069 MR2064316
3	A Bayer, Y I Manin, (Semi)simple exercises in quantum cohomology, from: "The Fano Conference" (editors A Collino, A Conte, M Marchisio), Univ. Torino (2004) 143 MR2112573
4	N Bourbaki, Algebra II: Chapters 4–7, Elements of Math., Springer (2003) MR1994218
5	D Calegari, scl, MSJ Memoirs 20, Math. Soc. of Japan (2009) MR2527432
6	C H Cho, Non-displaceable Lagrangian submanifolds and Floer cohomology with non-unitary line bundle, J. Geom. Phys. 58 (2008) 1465 MR2463805
7	G Ciolli, On the quantum cohomology of some Fano threefolds and a conjecture of Dubrovin, Internat. J. Math. 16 (2005) 823 MR2168069
8	T Delzant, Hamiltoniens périodiques et images convexes de l'application moment, Bull. Soc. Math. France 116 (1988) 315 MR984900
9	B Dubrovin, Geometry and analytic theory of Frobenius manifolds, from: "Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998)" (1998) 315 MR1648082
10	D Eisenbud, Commutative algebra with a view toward algebraic geometry, Graduate Texts in Math. 150, Springer (1995) MR1322960
11	Y Eliashberg, L Polterovich, Symplectic quasi-states on the quadric surface and Lagrangian submanifolds arXiv:1006.2501
12	M Entov, L Polterovich, Calabi quasimorphism and quantum homology, Int. Math. Res. Not. (2003) 1635 MR1979584
13	M Entov, L Polterovich, Quasi-states and symplectic intersections, Comment. Math. Helv. 81 (2006) 75 MR2208798
14	M Entov, L Polterovich, Symplectic quasi-states and semi-simplicity of quantum homology, from: "Toric topology" (editors M Harada, Y Karshon, M Masuda, T Panov), Contemp. Math. 460, Amer. Math. Soc. (2008) 47 MR2428348
15	M Entov, L Polterovich, Rigid subsets of symplectic manifolds, Compos. Math. 145 (2009) 773 MR2507748
16	M Entov, L Polterovich, F Zapolsky, Quasi-morphisms and the Poisson bracket, Pure Appl. Math. Q. 3 (2007) 1037 MR2402596
17	A Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988) 775 MR948771
18	A Floer, H Hofer, D Salamon, Transversality in elliptic Morse theory for the symplectic action, Duke Math. J. 80 (1995) 251 MR1360618
19	K Fukaya, Floer homology for families—a progress report, from: "Integrable systems, topology, and physics (Tokyo, 2000)" (editors M Guest, R Miyaoka, Y Ohnita), Contemp. Math. 309, Amer. Math. Soc. (2002) 33 MR1953352
20	K Fukaya, Y G Oh, H Ohta, K Ono, Spectral invariants with bulk, quasimorphisms and Lagrangian Floer theory arXiv:1105.5123
21	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory: Anomaly and obstruction. Parts I–II, AMS/IP Studies in Adv. Math., Amer. Math. Soc. (2009) MR2553465
22	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian Floer theory on compact toric manifolds. I, Duke Math. J. 151 (2010) 23 MR2573826
23	K Fukaya, K Ono, Arnold conjecture and Gromov–Witten invariant, Topology 38 (1999) 933 MR1688434
24	A Gathmann, Gromov–Witten invariants of blow-ups, J. Algebraic Geom. 10 (2001) 399 MR1832328
25	A Grothendieck, Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. I, Inst. Hautes Études Sci. Publ. Math. (1964) 259 MR0173675
26	A Grothendieck, Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas IV, Inst. Hautes Études Sci. Publ. Math. (1967) 361 MR0238860
27	R Hartshorne, Algebraic geometry, Graduate Texts in Math. 52, Springer (1977) MR0463157
28	C Hertling, Y I Manin, C Teleman, An update on semisimple quantum cohomology and $F$–manifolds, Tr. Mat. Inst. Steklova 264 (2009) 69 MR2590836
29	H Hofer, D A Salamon, Floer homology and Novikov rings, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 483 MR1362838
30	H Hofer, C Viterbo, The Weinstein conjecture in the presence of holomorphic spheres, Comm. Pure Appl. Math. 45 (1992) 583 MR1162367
31	H Hofer, K Wysocki, E Zehnder, A general Fredholm theory. I: A splicing-based differential geometry, J. Eur. Math. Soc. 9 (2007) 841 MR2341834
32	J Hu, Gromov–Witten invariants of blow-ups along points and curves, Math. Z. 233 (2000) 709 MR1759269
33	H Iritani, Convergence of quantum cohomology by quantum Lefschetz, J. Reine Angew. Math. 610 (2007) 29 MR2359850
34	M Kontsevich, Y Manin, Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994) 525 MR1291244
35	H V Lê, K Ono, Cup-length estimates for symplectic fixed points, from: "Contact and symplectic geometry (Cambridge, 1994)" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 268 MR1432466
36	J Li, G Tian, Virtual moduli cycles and Gromov–Witten invariants of general symplectic manifolds, from: "Topics in symplectic $4$–manifolds (Irvine, CA, 1996)" (editor R J Stern), First Int. Press Lect. Ser. 1, Int. Press (1998) 47 MR1635695
37	G Liu, G Tian, Floer homology and Arnold conjecture, J. Differential Geom. 49 (1998) 1 MR1642105
38	G Liu, G Tian, Weinstein conjecture and GW–invariants, Commun. Contemp. Math. 2 (2000) 405 MR1806943
39	G Lu, An explicit isomorphism between Floer homology and quantum homology, Pacific J. Math. 213 (2004) 319 MR2036923
40	G Lu, Gromov–Witten invariants and pseudo symplectic capacities, Israel J. Math. 156 (2006) 1 MR2282367
41	Y I Manin, Frobenius manifolds, quantum cohomology, and moduli spaces, Amer. Math. Soc. Colloq. Publ. 47, Amer. Math. Soc. (1999) MR1702284
42	H Matsumura, Commutative algebra, Math. Lecture Note Ser. 56, Benjamin/Cummings (1980) MR575344
43	D McDuff, Hamiltonian $S^1$–manifolds are uniruled, Duke Math. J. 146 (2009) 449 MR2484280
44	D McDuff, D Salamon, $J$–holomorphic curves and symplectic topology, Amer. Math. Soc. Colloq. Publ. 52, Amer. Math. Soc. (2004) MR2045629
45	Y G Oh, Spectral invariants and the length minimizing property of Hamiltonian paths, Asian J. Math. 9 (2005) 1 MR2150687
46	Y G Oh, Lectures on Floer theory and spectral invariants of Hamiltonian flows, from: "Morse theoretic methods in nonlinear analysis and in symplectic topology" (editors P Biran, O Cornea, F Lalonde), NATO Sci. Ser. II Math. Phys. Chem. 217, Springer (2006) 321 MR2276955
47	Y G Oh, K Zhu, Floer trajectories with immersed nodes and scale-dependent gluing arXiv:0711.4187
48	Y Ostrover, I Tyomkin, On the quantum homology algebra of toric Fano manifolds, Selecta Math. $($N.S.$)$ 15 (2009) 121 MR2511201
49	S Piunikhin, D Salamon, M Schwarz, Symplectic Floer–Donaldson theory and quantum cohomology, from: "Contact and symplectic geometry (Cambridge, 1994)" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 171 MR1432464
50	G Pólya, G Szegő, Problems and theorems in analysis. I: Series, integral calculus, theory of functions, Grund. der Math. Wissenschaften 193, Springer (1978) MR580154
51	A F Ritter, Novikov-symplectic cohomology and exact Lagrangian embeddings, Geom. Topol. 13 (2009) 943 MR2470967
52	J Robbin, D Salamon, The Maslov index for paths, Topology 32 (1993) 827 MR1241874
53	Y Ruan, Virtual neighborhoods and pseudo-holomorphic curves, from: "Proceedings of 6th Gökova Geometry-Topology Conference", Turkish J. Math. 23 (1999) 161 MR1701645
54	Y Ruan, G Tian, A mathematical theory of quantum cohomology, J. Differential Geom. 42 (1995) 259 MR1366548
55	D Salamon, Lectures on Floer homology, from: "Symplectic geometry and topology (Park City, UT, 1997)" (editors Y Eliashberg, L Traynor), IAS/Park City Math. Ser. 7, Amer. Math. Soc. (1999) 143 MR1702944
56	M Schwarz, Cohomology operations from $S^1$–cobordisms in Floer homology, PhD thesis, ETH Zürich (1995)
57	M Schwarz, On the action spectrum for closed symplectically aspherical manifolds, Pacific J. Math. 193 (2000) 419 MR1755825
58	The Stacks Project Authors, The stacks project
59	R Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954) 17 MR0061823
60	M Usher, Spectral numbers in Floer theories, Compos. Math. 144 (2008) 1581 MR2474322
61	M Usher, Duality in filtered Floer–Novikov complexes, J. Topol. Anal. 2 (2010) 233 MR2652908
62	M Usher, The sharp energy-capacity inequality, Commun. Contemp. Math. 12 (2010) 457 MR2661273
63	M Usher, Boundary depth in Hamiltonian Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds, Israel J. Math. 184 (2011) 1
64	E Witten, On the structure of the topological phase of two-dimensional gravity, Nuclear Phys. B 340 (1990) 281 MR1068086
65	E Witten, Two-dimensional gravity and intersection theory on moduli space, from: "Surveys in differential geometry (Cambridge, MA, 1990)", Lehigh Univ. (1991) 243 MR1144529