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

Volume 26
Issue 5, 1597–1963
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 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
Exact Lagrangian tori in symplectic Milnor fibers constructed with fillings

Orsola Capovilla-Searle

Algebraic & Geometric Topology 25 (2025) 3225–3249
Bibliography
1 M Abouzaid, I Smith, Exact Lagrangians in plumbings, Geom. Funct. Anal. 22 (2012) 785 MR2984118
2 B Acu, O Capovilla-Searle, A Gadbled, A Marinković, E Murphy, L Starkston, A Wu, Weinstein handlebodies for complements of smoothed toric divisors, 1561, Amer. Math. Soc. (2025) MR4913463
3 V I Arnold, V A Vasilev, V V Goryunov, O V Lyashko, Dynamical systems, VI, 6, Springer (1993) MR1230637
4 F Bourgeois, T Ekholm, Y Eliashberg, Effect of Legendrian surgery, Geom. Topol. 16 (2012) 301 MR2916289
5 O Capovilla-Searle, R Casals, On Newton polytopes of Lagrangian augmentations, Bull. Lond. Math. Soc. 56 (2024) 1263 MR4735617
6 O Capovilla-Searle, N Legout, M Limouzineau, E Murphy, Y Pan, L Traynor, Obstructions to reversing Lagrangian surgery in Lagrangian fillings, J. Symplectic Geom. 22 (2024) 599
7 R Casals, E Murphy, Legendrian fronts for affine varieties, Duke Math. J. 168 (2019) 225 MR3909897
8 R Casals, L Ng, Braid loops with infinite monodromy on the Legendrian contact DGA, J. Topol. 15 (2022) 1927 MR4584583
9 B Chantraine, Lagrangian concordance of Legendrian knots, Algebr. Geom. Topol. 10 (2010) 63 MR2580429
10 B Chantraine, G Dimitroglou Rizell, P Ghiggini, R Golovko, Geometric generation of the wrapped Fukaya category of Weinstein manifolds and sectors, Ann. Sci. École Norm. Sup. 57 (2024) 1 MR4732675
11 Y Chekanov, Differential algebra of Legendrian links, Invent. Math. 150 (2002) 441 MR1946550
12 K Cieliebak, Handle attaching in symplectic homology and the chord conjecture, J. Eur. Math. Soc. 4 (2002) 115 MR1911873
13 K Cieliebak, Y Eliashberg, From Stein to Weinstein and back : symplectic geometry of affine complex manifolds, 59, Amer. Math. Soc. (2012) MR3012475
14 F Ding, H Geiges, Handle moves in contact surgery diagrams, J. Topol. 2 (2009) 105 MR2499439
15 A H Durfee, Fifteen characterizations of rational double points and simple critical points, Enseign. Math. 25 (1979) 131 MR543555
16 T Ekholm, Holomorphic curves for Legendrian surgery, preprint (2019) arXiv:1906.07228
17 T Ekholm, J Etnyre, M Sullivan, The contact homology of Legendrian submanifolds in 2n+1, J. Differential Geom. 71 (2005) 177 MR2197142
18 T Ekholm, J Etnyre, M Sullivan, Orientations in Legendrian contact homology and exact Lagrangian immersions, Internat. J. Math. 16 (2005) 453 MR2141318
19 T Ekholm, K Honda, T Kálmán, Legendrian knots and exact Lagrangian cobordisms, J. Eur. Math. Soc. 18 (2016) 2627 MR3562353
20 T Ekholm, L Ng, Legendrian contact homology in the boundary of a subcritical Weinstein 4-manifold, J. Differential Geom. 101 (2015) 67 MR3356070
21 Y Eliashberg, Topological characterization of Stein manifolds of dimension > 2, Internat. J. Math. 1 (1990) 29 MR1044658
22 Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, Geom. Funct. Anal. (2000) 560 MR1826267
23 Y Eliashberg, L Polterovich, Local Lagrangian 2-knots are trivial, Ann. of Math. 144 (1996) 61 MR1405943
24 J B Etnyre, L L Ng, Legendrian contact homology in 3, from: "Surveys in 3-manifold topology and geometry", Surv. Differ. Geom. 25, International (2022) 103 MR4479751
25 E Giroux, J Pardon, Existence of Lefschetz fibrations on Stein and Weinstein domains, Geom. Topol. 21 (2017) 963 MR3626595
26 R E Gompf, Handlebody construction of Stein surfaces, Ann. of Math. 148 (1998) 619 MR1668563
27 P Hacking, A Keating, Homological mirror symmetry for log Calabi–Yau surfaces, Geom. Topol. 26 (2022) 3747 MR4562569
28 A Ishii, K Ueda, H Uehara, Stability conditions on An-singularities, J. Differential Geom. 84 (2010) 87 MR2629510
29 C Karlsson, A note on coherent orientations for exact Lagrangian cobordisms, Quantum Topol. 11 (2020) 1 MR4071329
30 A M Keating, Dehn twists and free subgroups of symplectic mapping class groups, J. Topol. 7 (2014) 436 MR3217627
31 A Keating, Lagrangian tori in four-dimensional Milnor fibres, Geom. Funct. Anal. 25 (2015) 1822 MR3432159
32 A Keating, Homological mirror symmetry for hypersurface cusp singularities, Selecta Math. 24 (2018) 1411 MR3782425
33 A Keating, Families of monotone Lagrangians in Brieskorn–Pham hypersurfaces, Math. Ann. 380 (2021) 975 MR4297180
34 C Leverson, Augmentations and rulings of Legendrian links in #k(S1 × S2), Pacific J. Math. 288 (2017) 381 MR3646897
35 M McLean, Lefschetz fibrations and symplectic homology, Geom. Topol. 13 (2009) 1877 MR2497314
36 J Milnor, Singular points of complex hypersurfaces, 61, Princeton Univ. Press (1968) MR239612
37 Y Pan, D Rutherford, Functorial LCH for immersed Lagrangian cobordisms, J. Symplectic Geom. 19 (2021) 635 MR4325415
38 P Seidel, Fukaya categories and Picard–Lefschetz theory, Eur. Math. Soc. (2008) MR2441780
39 V Shende, D Treumann, H Williams, On the combinatorics of exact Lagrangian surfaces, preprint (2016) arXiv:1603.07449
40 S Sivek, The contact homology of Legendrian knots with maximal Thurston–Bennequin invariant, J. Symplectic Geom. 11 (2013) 167 MR3046489
41 R Vianna, Infinitely many monotone Lagrangian tori in del Pezzo surfaces, Selecta Math. 23 (2017) 1955 MR3663599
42 A Weinstein, Contact surgery and symplectic handlebodies, Hokkaido Math. J. 20 (1991) 241 MR1114405