We prove a new finiteness result for the Hofer–Zehnder capacity of certain unit disk cotangent bundles. It is proved by a computation of the pair-of-pants product on Floer homology of cotangent bundles, combined with the theory of spectral invariants. The computation of the pair-of-pants product is reduced to a simple key computation of the Chas–Sullivan loop product.
Cite this article
Kei Irie, Hofer–Zehnder capacity of unit disk cotangent bundles and the loop product. J. Eur. Math. Soc. 16 (2014), no. 11, pp. 2477–2497