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A relative version of Weinstein's morphism
Abstract
We introduce a relative version of Weinstein's morphism associated to a Lagrangian submanifold L of a closed symplectic manifold (M,ω). We construct a homomorphism 𝒜(L,α): π1(Ham0(M,L)) ⟶ ℝ/𝒫2(M,ω), and establish its basic properties. We compute the invariant in several examples, including latitude circles in S2, and more generally, Lagrangian fibers in toric manifolds. These computations provide obstructions to Ha\-mil\-to\-nian isotopy of Lagrangian submanifolds and detect nontrivial, and in some cases infinite-order, elements in the homotopy groups of their Hamiltonian stabilizers.
Related
- The Relative Differential Morphism and the Logarithmic Connection of Dual Conformal Nets
- Generalized Marsden-Weinstein symplectic structures
- Decompositions and diagrams of symplectic surfaces in Weinstein domains
- Decompositions of birational toric morphism between threefolds
- On the size of the fibers of a morphism of algebraic varieties
BibTeX
@misc{pedroza2026relative,
title = {{A relative version of Weinstein's morphism}},
author = {Andrés Pedroza and Daniel Villanueva-Vega},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01083},
eprint = {2611.01083},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01083},
}
RIS
TY - UNPB
TI - A relative version of Weinstein's morphism
AU - Andrés Pedroza
AU - Daniel Villanueva-Vega
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01083
UR - https://arxiv.org/abs/2611.01083
AB - We introduce a relative version of Weinstein's morphism associated to a Lagrangian submanifold L of a closed symplectic manifold (M,ω). We construct a homomorphism 𝒜^(L,α): π_1(Ham_0(M,L)) ⟶ ℝ/𝒫_2(M,ω), and establish its basic properties. We compute the invariant in several examples, including latitude circles in S^2, and more generally, Lagrangian fibers in toric manifolds. These computations provide obstructions to Ha\-mil\-to\-nian isotopy of Lagrangian submanifolds and detect nontrivial, and in some cases infinite-order, elements in the homotopy groups of their Hamiltonian stabilizers.
ER -