On analytical applications of stable homotopy (the Arnold conjecture, critical points)

TL;DR

This paper proves the Arnold conjecture for certain symplectic manifolds and establishes an analog of the Lusternik-Schnirelmann theorem for functions with generalized hyperbolicity, advancing the understanding of critical points in symplectic topology.

Contribution

It provides a proof of the Arnold conjecture for closed symplectic manifolds with specific topological conditions and introduces a new theorem related to generalized hyperbolicity.

Findings

Proof of the Arnold conjecture for manifolds with $ ext{pi}_2(M)=0$ and $ ext{cat} M= ext{dim} M$

An analog of the Lusternik-Schnirelmann theorem for generalized hyperbolic functions

Enhanced understanding of critical points in symplectic topology

Abstract

We prove the Arnold conjecture for closed symplectic manifolds with $\pi_2(M)=0$ and $\cat M=\dim M$. Furthermore, we prove an analog of the Lusternik-Schnirelmann theorem for functions with ``generalized hyperbolicity'' property.