Hofer-Zehnder capacity of unit disk cotangent bundles and the loop product

TL;DR

This paper establishes the finiteness of the Hofer-Zehnder capacity for unit disk cotangent bundles of closed Riemannian manifolds by linking Floer homology pair-of-pants products to loop products, under certain topological conditions.

Contribution

It provides a novel computation connecting Floer homology pair-of-pants products with loop products, demonstrating capacity finiteness under new topological assumptions.

Findings

Hofer-Zehnder capacity is finite for certain cotangent bundles.

The pair-of-pants product on Floer homology is computed explicitly.

Reduction to loop product simplifies the capacity analysis.

Abstract

We prove the finiteness of the Hofer-Zehnder capacity of unit disk cotangent bundles of closed Riemannian manifolds, under some simple topological assumptions on the manifolds. The key ingredient of the proof is a computation of the pair-of-pants product on Floer homology of cotangent bundles. We reduce it to a simple computation of the loop product, making use of results of A.Abbondandolo- M.Schwarz.