부산대학교 도서관

This paper contains a proof of Gromov's nonsqueezing theorem, giving a necessary and sufficient condition for a symplectic embedding of a ball into a cylinder. The result is well known, and the scheme of the proof here goes back to M.~Gromov's original paper [Invent. Math. {\bf 82} (1985), no.~2, 307--347; MR0809718]. This involves showing that a certain moduli space of pseudoholomorphic spheres, or a perturbation of the moduli space, has the structure of a smooth cobordism, and the novelty of the article is that this is done using the machinery of polyfolds, following [H.~H.~W. Hofer, K. Wysocki and E.~J. Zehnder, Mem. Amer. Math. Soc. {\bf 248} (2017), no.~1179, v+218 pp.; MR3683060]. \par The authors carefully construct an M-polyfold structure on a suitable space ${[0,1]\times\Cal{B}}$ of maps modulo reparameterization, an M-polyfold bundle $\Cal{E}$ over $[0,1]\times\Cal{B}$, and an sc@-Fredholm section $\sigma\:[0,1]\times\Cal{B}\to\Cal{E}$ whose zero set is the moduli space of interest. Then a general polyfold regularization theorem is applied to perturb $\sigma$ such that its zero set is a smooth cobordism as required. The proofs should provide a model for arguments of similar kinds requiring polyfold methods.