Hirzebruch genera of manifolds equipped with a Hamiltonian circle action

TL;DR

This paper investigates obstructions to symplectic and Hamiltonian circle actions on compact manifolds using Hirzebruch genera, linking differential and homotopic invariants to understand these symmetries.

Contribution

It introduces new obstructions based on Hirzebruch genera for the existence of Hamiltonian circle actions on manifolds.

Findings

Identifies specific Hirzebruch genus relations that obstruct circle actions

Establishes connections between differential invariants and homotopic properties

Provides criteria for the non-existence of certain symplectic actions

Abstract

In the paper we describe obstructions for the existence of symplectic and Hamiltonian symplectic circle actions on closed compact manifolds in terms of Hirzebruch genera and relations between differential and homotopic invariants of such manifolds.