Algebraic & Geometric Topology Volume 25, issue 3 (2025)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

Hamiltonian classification of toric fibres and symmetric probes

Joé Brendel

Algebraic & Geometric Topology 25 (2025) 1839–1876

DOI: 10.2140/agt.2025.25.1839

Bibliography

1	M Abreu, M S Borman, D McDuff, Displacing Lagrangian toric fibers by extended probes, Algebr. Geom. Topol. 14 (2014) 687 MR3159967
2	M Abreu, L Macarini, Remarks on Lagrangian intersections in toric manifolds, Trans. Amer. Math. Soc. 365 (2013) 3851 MR3042606
3	M Audin, Torus actions on symplectic manifolds, 93, Birkhäuser (2004) MR2091310
4	M Augustynowicz, J Smith, J Wornbard, Homological Lagrangian monodromy for some monotone tori, Quantum Topol. (2024)
5	D Auroux, Infinitely many monotone Lagrangian tori in ℝ⁶, Invent. Math. 201 (2015) 909 MR3385637
6	J Brendel, Real Lagrangian tori and versal deformations, J. Symplectic Geom. 21 (2023) 463 MR4687581
7	J Brendel, J Kim, On Lagrangian tori in S² × S² and billiards, preprint (2025) arXiv:2502.03324
8	J Brendel, J Kim, J Moon, On the topology of real Lagrangians in toric symplectic manifolds, Israel J. Math. 253 (2023) 113 MR4575406
9	J Brendel, G Mikhalkin, F Schlenk, Non-isotopic symplectic embeddings of cubes, in preparation
10	L M Cabrer, D Mundici, Classifying GL(n, ℤ)-orbits of points and rational subspaces, Discrete Contin. Dyn. Syst. 36 (2016) 4723 MR3541502
11	A Cannas da Silva, Symplectic toric manifolds, from: "Symplectic geometry of integrable Hamiltonian systems", Birkhäuser (2003) 85 MR2000746
12	Y V Chekanov, Lagrangian tori in a symplectic vector space and global symplectomorphisms, Math. Z. 223 (1996) 547 MR1421954
13	Y V Chekanov, Lagrangian intersections, symplectic energy, and areas of holomorphic curves, Duke Math. J. 95 (1998) 213 MR1646550
14	Y Chekanov, F Schlenk, Notes on monotone Lagrangian twist tori, Electron. Res. Announc. Math. Sci. 17 (2010) 104 MR2735030
15	Y Chekanov, F Schlenk, Lagrangian product tori in symplectic manifolds, Comment. Math. Helv. 91 (2016) 445 MR3541716
16	C H Cho, Non-displaceable Lagrangian submanifolds and Floer cohomology with non-unitary line bundle, J. Geom. Phys. 58 (2008) 1465 MR2463805
17	J S Dani, Density properties of orbits under discrete groups, J. Indian Math. Soc. 39 (1975) 189 MR444570
18	T Delzant, Hamiltoniens périodiques et images convexes de l’application moment, Bull. Soc. Math. France 116 (1988) 315 MR984900
19	K Fukaya, Y G Oh, H Ohta, K Ono, Displacement of polydisks and Lagrangian Floer theory, J. Symplectic Geom. 11 (2013) 231 MR3046491
20	V Guillemin, Moment maps and combinatorial invariants of Hamiltonian Tⁿ-spaces, 122, Birkhäuser (1994) MR1301331
21	S Hu, F Lalonde, R Leclercq, Homological Lagrangian monodromy, Geom. Topol. 15 (2011) 1617 MR2851073
22	C Y Mak, I Smith, Non-displaceable Lagrangian links in four-manifolds, Geom. Funct. Anal. 31 (2021) 438 MR4268306
23	D McDuff, Displacing Lagrangian toric fibers via probes, from: "Low-dimensional and symplectic topology", Proc. Sympos. Pure Math. 82, Amer. Math. Soc. (2011) 131 MR2768658
24	D McDuff, D Salamon, Introduction to symplectic topology, Oxford Univ. Press (2017) MR3674984
25	L Polterovich, The geometry of the group of symplectic diffeomorphisms, Birkhäuser (2001) MR1826128
26	N W Porcelli, Families of relatively exact Lagrangians, free loop spaces and generalised homology, Selecta Math. 30 (2024) 21 MR4700425
27	E Shelukhin, D Tonkonog, R Vianna, Geometry of symplectic flux and Lagrangian torus fibrations, preprint (2018) arXiv:1804.02044
28	J Smith, A monotone Lagrangian casebook, Algebr. Geom. Topol. 21 (2021) 2273 MR4334513
29	S M Trott, A pair of generators for the unimodular group, Canad. Math. Bull. 5 (1962) 245 MR141716
30	R Vianna, Infinitely many exotic monotone Lagrangian tori in ℂℙ², J. Topol. 9 (2016) 535 MR3509972
31	R Vianna, Infinitely many monotone Lagrangian tori in del Pezzo surfaces, Selecta Math. 23 (2017) 1955 MR3663599
32	M L Yau, Monodromy and isotopy of monotone Lagrangian tori, Math. Res. Lett. 16 (2009) 531 MR2511631