Symplectic fixed points and Lagrangian intersections on weighted projective spaces

TL;DR

This paper extends the validity of Arnold's conjecture to weighted projective spaces, demonstrating that Hamiltonian fixed points and Lagrangian intersections behave as predicted under certain conditions.

Contribution

It proves Arnold's conjecture for Hamiltonian maps on weighted projective spaces and for Lagrangian intersections when all weights are odd.

Findings

Arnold conjecture holds on weighted projective spaces for Hamiltonian maps.

Arnold conjecture for Lagrangian intersections holds if all weights are odd.

The results generalize classical symplectic topology conjectures to weighted spaces.

Abstract

In this note we observe that Arnold conjecture for the Hamiltonian maps still holds on weighted projective spaces $\CP^n({\bf q})$, and that Arnold conjecture for the Lagrange intersections for $(\CP^n({\bf q}), \RP^n({\bf q}))$ is also true if each weight $q_i\in {\bf q}=\{q_1,..., q_{n+1}\}$ is odd.