Generalization of Weinstein's Morphism
Symplectic Geometry
2025-11-24 v1
Abstract
We introduce a generalization of Weinstein's morphism, defined on \pi_{2k-1}(Ham(M,\omega)) for 1 < k \leq n, where (M,\omega) is a 2n-dimensional symplectic manifold. Using this morphism, we show that for n > 1 and 1 < k \leq n, the homotopy groups \pi_{2k-1}(Ham(CP^n,\omega_{FS})) and \pi_{2k-1}(Ham(\tilde CP^n,\tilde\omega_\rho)) are nontrivial. Here, (\tilde CP^n,\tilde\omega_\rho) denotes the symplectic one-point blow-up of (CP^n,\omega_FS) of weigh \rho.
Keywords
Cite
@article{arxiv.2511.16914,
title = {Generalization of Weinstein's Morphism},
author = {Andrés Pedroza},
journal= {arXiv preprint arXiv:2511.16914},
year = {2025}
}
Comments
This manuscript is an improved and corrected version of the preprint arXiv:2312.05091