Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/0602475

Isotopies of high genus Lagrangian surfaces

R. Hind·A. Ivrii
View original source ↗Read source document ↗Export metadata ↓

Abstract

We show that all Lagrangian submanifolds of the cotangent bundle of a Riemann surface which are homotopic to the zero section must be smoothly isotopic to the zero section.

Explore related subjects

math.SG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

R. Hind, A. Ivrii. 2006-02-21. Isotopies of high genus Lagrangian surfaces. https://arxiv.org/abs/math/0602475

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Algebra of the Infrared with Elliptic Curve-Valued Potential

We study an extension of the algebra of the infrared to curve--valued potentials, focusing on the elliptic curve case. Given a finite configuration of points on an elliptic curve, we construct associated \(L_\infty\)-algebra. Adding an extra point produces a directed \(A_\infty\)-algebra and an \(L_\infty\)-morphism to their directed Hochschild deformation complexes. Maurer--Cartan elements of the \(L_\infty\)-algebra determine \(A_\infty\)-deformations of the directed algebra. We formulate a conjectural comparison between Maurer--Cartan deformations of the directed algebra and the directed Fukaya--Seidel category associated to compatible finite collections of thimbles.

math.SG↗
arXiv2026

Moment Lagrangians, unobstructedness and symplectic groupoids

Moment Lagrangian $L_μ$ is a Lagrangian in $T^*G^- \times Y^- \times Y$ associated to a Hamiltonian $G$-space $Y$ with a moment map $μ$. In this paper, we prove that $L_μ$ is tautologically unobstructed under mild assumptions on $Y$. As a key ingredient in the proof, we constructed a new symplectic groupoid structure on $T^*G^- \times Y^- \times Y$ over $G\times Y$ for which $L_μ$ is simultaneously the unit and the fixed locus of the inversion, which might be of independent interest.

math.SG↗
arXiv2026

Functors from Lagrangian correspondences for wrapped sheaf categories

We consider the category of sheaves on a manifold with microsupport in a singular conic Lagrangian, and more generally microsheaves on the Lagrangian skeleton of a Weinstein manifold with stop, which are equivalent to ind-completions of partially wrapped Fukaya categories. Compact objects in these categories are obtained as wrappings of constructible sheaves with perfect stalks; they correspond to objects built from exact Lagrangians in finitely many steps. We give a microlocal criterion on constructible (micro)sheaves with perfect (micro)stalks which guarantees that the corresponding wrapped sheaves induce integral kernels that preserve compact objects of these categories. This generalizes a result of Gao on Lagrangian correspondences between fully wrapped Fukaya categories.

math.SG↗