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.
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Kei Irie, Hofer–Zehnder capacity of unit disk cotangent bundles and the loop product. J. Eur. Math. Soc. 16 (2014), no. 11, pp. 2477–2497DOI 10.4171/JEMS/491