Algebraic & Geometric Topology Volume 21, issue 5 (2021)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Invariance of immersed Floer cohomology under Maslov flows

Joseph Palmer and Chris Woodward

Algebraic & Geometric Topology 21 (2021) 2313–2410

DOI: 10.2140/agt.2021.21.2313

Bibliography

1	M Abouzaid, Framed bordism and Lagrangian embeddings of exotic spheres, Ann. of Math. 175 (2012) 71 MR2874640
2	M Akaho, D Joyce, Immersed Lagrangian Floer theory, J. Differential Geom. 86 (2010) 381 MR2785840
3	G Alston, E Bao, Exact, graded, immersed Lagrangians and Floer theory, J. Symplectic Geom. 16 (2018) 357 MR3834425
4	S B Angenent, Curve shortening and the topology of closed geodesics on surfaces, Ann. of Math. 162 (2005) 1187 MR2179729
5	S B Angenent, J J L Velázquez, Asymptotic shape of cusp singularities in curve shortening, Duke Math. J. 77 (1995) 71 MR1317628
6	D Auroux, D Gayet, J P Mohsen, Symplectic hypersurfaces in the complement of an isotropic submanifold, Math. Ann. 321 (2001) 739 MR1872527
7	C Baker, The mean curvature flow of submanifolds of high codimension, preprint (2011) arXiv:1104.4409
8	P Biran, O Cornea, Quantum structures for Lagrangian submanifolds, preprint (2007) arXiv:0708.4221
9	R Bott, L W Tu, Differential forms in algebraic topology, 82, Springer (1982) MR658304
10	S. Carapetis, Curve-shortening flow: an interactive visualization, applet (2018)
11	J Cerf, La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie, Inst. Hautes Études Sci. Publ. Math. 39 (1970) 5 MR292089
12	F Charest, Source spaces and perturbations for cluster complexes, preprint (2012) arXiv:1212.2923
13	F Charest, C T Woodward, Floer theory and flips, preprint (2015) arXiv:1508.01573
14	F Charest, C Woodward, Floer trajectories and stabilizing divisors, J. Fixed Point Theory Appl. 19 (2017) 1165 MR3659006
15	J Chen, J M S Ma, Geometry of Lagrangian self-shrinking tori and applications to the piecewise Lagrangian mean curvature flow, preprint (2016) arXiv:1604.07563
16	W Chen, Y Ruan, Orbifold Gromov–Witten theory, from: "Orbifolds in mathematics and physics" (editors A Adem, J Morava, Y Ruan), Contemp. Math. 310, Amer. Math. Soc. (2002) 25 MR1950941
17	K Cieliebak, E Goldstein, A note on the mean curvature, Maslov class and symplectic area of Lagrangian immersions, J. Symplectic Geom. 2 (2004) 261 MR2108376
18	K Cieliebak, K Mohnke, Symplectic hypersurfaces and transversality in Gromov–Witten theory, J. Symplectic Geom. 5 (2007) 281 MR2399678
19	T H Colding, W P Minicozzi II, Generic mean curvature flow, I : Generic singularities, Ann. of Math. 175 (2012) 755 MR2993752
20	O Cornea, F Lalonde, Cluster homology: an overview of the construction and results, Electron. Res. Announc. Amer. Math. Soc. 12 (2006) 1 MR2200949
21	Darkdadaah, A simple monochrome sphere, (2005)
22	P Deligne, D S Freed, Sign manifesto, from: "Quantum fields and strings: a course for mathematicians, I" (editors P Deligne, P Etingof, D S Freed, L Jeffrey, D Kazhdan, J Morgan, D R Morrison, E Witten), Amer. Math. Soc. (1999) 357 MR1701601
23	S K Donaldson, Symplectic submanifolds and almost-complex geometry, J. Differential Geom. 44 (1996) 666 MR1438190
24	T Ekholm, J Etnyre, M Sullivan, The contact homology of Legendrian submanifolds in ℝ²ⁿ⁺¹, J. Differential Geom. 71 (2005) 177 MR2197142
25	T Ekholm, J Etnyre, M Sullivan, Orientations in Legendrian contact homology and exact Lagrangian immersions, Internat. J. Math. 16 (2005) 453 MR2141318
26	K Y Fang, Geometric constructions of mapping cones in the Fukaya category, PhD thesis, University of California, Berkeley (2017) MR3781744
27	A Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988) 513 MR965228
28	A Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988) 775 MR948771
29	A Floer, Monopoles on asymptotically flat manifolds, from: "The Floer memorial volume" (editors H Hofer, C H Taubes, A Weinstein, E Zehnder), Progr. Math. 133, Birkhäuser (1995) 3 MR1362821
30	U Frauenfelder, K Zehmisch, Gromov compactness for holomorphic discs with totally real boundary conditions, J. Fixed Point Theory Appl. 17 (2015) 521 MR3411803
31	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory : anomaly and obstruction, I, 46, Amer. Math. Soc. (2009) MR2553465
32	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory : anomaly and obstruction, II, 46, Amer. Math. Soc. (2009) MR2548482
33	K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian Floer theory on compact toric manifolds, I, Duke Math. J. 151 (2010) 23 MR2573826
34	S. Ganatra, Symplectic cohomology and duality for the wrapped Fukaya category, PhD thesis, Massachusetts Institute of Technology (2006)
35	M A Grayson, The heat equation shrinks embedded plane curves to round points, J. Differential Geom. 26 (1987) 285 MR906392
36	M A Grayson, The shape of a figure-eight under the curve shortening flow, Invent. Math. 96 (1989) 177 MR981740
37	M L Gromov, A topological technique for the construction of solutions of differential equations and inequalities, from: "Actes du Congrès International des Mathématiciens, II" (editors M Berger, J Dieudonné, J Leray, J L Lions, P Malliavin, J P Serre), Gauthier-Villars (1971) 221 MR0411875
38	D Joyce, Conjectures on Bridgeland stability for Fukaya categories of Calabi–Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow, EMS Surv. Math. Sci. 2 (2015) 1 MR3354954
39	D. Joyce, Lagrangian mean curvature flow in Calabi–Yau manifolds and the Thomas–Yau conjecture, II, talk slides (2017)
40	Y J Lee, Reidemeister torsion in Floer–Novikov theory and counting pseudo-holomorphic tori, I, J. Symplectic Geom. 3 (2005) 221 MR2199540
41	Y J Lee, Reidemeister torsion in Floer–Novikov theory and counting pseudo-holomorphic tori, II, J. Symplectic Geom. 3 (2005) 385 MR2198782
42	J A Lees, On the classification of Lagrange immersions, Duke Math. J. 43 (1976) 217 MR410764
43	J D Lotay, T Pacini, From Lagrangian to totally real geometry : coupled flows and calibrations, Comm. Anal. Geom. 28 (2020) 607 MR4124139
44	C Y Mak, W Wu, Dehn twist exact sequences through Lagrangian cobordism, Compos. Math. 154 (2018) 2485 MR3873526
45	D McDuff, D Salamon, J–holomorphic curves and symplectic topology, 52, Amer. Math. Soc. (2004) MR2045629
46	J Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965) 286 MR182927
47	T Pacini, Maslov, Chern–Weil and mean curvature, J. Geom. Phys. 135 (2019) 129 MR3872628
48	J Palmer, C Woodward, Invariance of immersed Floer cohomology under Lagrangian surgery, preprint (2019) arXiv:1903.01943
49	H L Royden, Real analysis, Macmillan (1988) MR1013117
50	F Schmäschke, Floer homology of Lagrangians in clean intersection, preprint (2016) arXiv:1606.05327
51	M Schwarz, Morse homology, 111, Birkhäuser (1993) MR1239174
52	P Seidel, Graded Lagrangian submanifolds, Bull. Soc. Math. France 128 (2000) 103 MR1765826
53	P Seidel, Homological mirror symmetry for the genus two curve, J. Algebraic Geom. 20 (2011) 727 MR2819674
54	J C Sikorav, Some properties of holomorphic curves in almost complex manifolds, from: "Holomorphic curves in symplectic geometry" (editors M Audin, J Lafontaine), Progr. Math. 117, Birkhäuser (1994) 165 MR1274929
55	K. Smoczyk, Lagrangian mean curvature flow, Habilitation thesis, Leipzig University (2001)
56	M G Sullivan, K–theoretic invariants for Floer homology, Geom. Funct. Anal. 12 (2002) 810 MR1935550
57	R P Thomas, S T Yau, Special Lagrangians, stable bundles and mean curvature flow, Comm. Anal. Geom. 10 (2002) 1075 MR1957663
58	S E Warschawski, On the higher derivatives at the boundary in conformal mapping, Trans. Amer. Math. Soc. 38 (1935) 310 MR1501813
59	K Wehrheim, C Woodward, Orientations for pseudoholomorphic quilts, preprint (2015) arXiv:1503.07803
60	C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324
61	A Weinstein, Removing intersections of Lagrangian immersions, Illinois J. Math. 27 (1983) 484 MR698310