Infinitely many monotone Lagrangian tori in del Pezzo surfaces

R Vianna - Selecta Mathematica, 2017 - Springer
We construct almost toric fibrations (ATFs) on all del Pezzo surfaces, endowed with a
monotone symplectic form. Except for CP^ 2\# CP^ 2 CP 2# CP 2¯, CP^ 2\# 2 CP^ 2 CP 2# 2 …

Lagrangian cobordisms in Liouville manifolds

V Bosshard - Journal of Topology and Analysis, 2024 - World Scientific
Floer theory for Lagrangian cobordisms was developed by Biran and Cornea in a series of
papers [Lagrangian cobordism. I, J. Amer. Math. Soc. 26 (2013) 295–340; Lagrangian …

Families of monotone Lagrangians in Brieskorn–Pham hypersurfaces

A Keating - Mathematische Annalen, 2021 - Springer
We present techniques, inspired by monodromy considerations, for constructing compact
monotone Lagrangians in certain affine hypersurfaces, chiefly of Brieskorn–Pham type. We …

Packing Lagrangian tori

RK Hind, E Kerman - arXiv preprint arXiv:2109.01772, 2021 - arxiv.org
In this paper we consider the problem of packing a symplectic manifold with integral
Lagrangian tori, that is Lagrangian tori whose area homomorphsims take only integer …

Infinitely many exotic Lagrangian tori in higher projective spaces

S Chanda, A Hirschi, L Wang - Journal of Fixed Point Theory and …, 2024 - Springer
Abstract In de Velloso Vianna (J Topol 9 (2): 535-551, 2016), Vianna constructed infinitely
many exotic Lagrangian tori in P 2. We lift these tori to higher dimensional projective spaces …

Lagrangian knots and unknots--an essay

L Polterovich, F Schlenk - arXiv preprint arXiv:2406.15967, 2024 - arxiv.org
In this essay dedicated to Yakov Eliashberg we survey the current state of the field of
Lagrangian (un) knots, reviewing some constructions and obstructions along with a number …

Unknottedness of real Lagrangian tori in

J Kim - Mathematische Annalen, 2020 - Springer
We prove the Hamiltonian unknottedness of real Lagrangian tori in the monotone S^ 2 * S^ 2
S 2× S 2, namely any real Lagrangian torus in S^ 2 * S^ 2 S 2× S 2 is Hamiltonian isotopic to …

Uniqueness of real Lagrangians up to cobordism

J Kim - International Mathematics Research Notices, 2021 - academic.oup.com
We prove that a real Lagrangian submanifold in a closed symplectic manifold is unique up to
cobordism. We then discuss the classification of real Lagrangians in and. In particular, we …

Lagrangian isotopies and symplectic function theory.

M Entov, Y Ganor, C Membrez - Commentarii Mathematici Helvetici, 2018 - ems.press
We study two related invariants of Lagrangian submanifolds in symplectic manifolds. For a
Lagrangian torus these invariants are functions on the first cohomology of the torus. The first …

Generalised cohomology and relatively exact Lagrangian submanifolds

N Porcelli - 2022 - repository.cam.ac.uk
In this thesis, we study the topology of relatively exact Lagrangian submanifolds. One of our
main goals is to study their generalised cohomology, extending known results about their …