Remark on the Betti numbers for Hamiltonian circle actions

TL;DR

This paper presents an inequality relating Betti numbers for closed Hamiltonian circle actions with isolated fixed points, contributing to the understanding of topological invariants in symplectic geometry.

Contribution

It introduces a new inequality involving Betti numbers for Hamiltonian $S^1$-manifolds with isolated fixed points, advancing the study of their topological properties.

Findings

Established a specific inequality for Betti numbers in this context

Provides new insights into the topology of Hamiltonian circle actions

Enhances understanding of fixed point contributions to Betti numbers

Abstract

In this paper, we establish a certain inequality in terms of Betti numbers of a closed Hamiltonian $S^1$-manifold with isolated fixed points.