Finiteness of $\pi_1$-sensitive Hofer-Zehnder capacity and equivariant loop space homology

TL;DR

This paper proves that for certain manifolds, the Hofer-Zehnder capacity of the cotangent bundle's unit disk bundle is finite, linking symplectic invariants to topological properties.

Contribution

It establishes the finiteness of the Hofer-Zehnder capacity for cotangent bundles of rationally inessential manifolds, connecting symplectic geometry and algebraic topology.

Findings

Hofer-Zehnder capacity is finite for cotangent bundles of rationally inessential manifolds

Links symplectic invariants with topological properties of manifolds

Provides new insights into the structure of symplectic capacities

Abstract

We prove that if M is a closed, connected, oriented, rationally inessential manifold, then the Hofer-Zehnder capacity of the unit disk bundle of the cotangent bundle of M is finite.