부산대학교 도서관

This paper contains a proof of Gromov's nonsqueezing theorem, giving anecessary and sufficient condition for a symplectic embedding of a ballinto a cylinder. The result is well known, and the scheme of the proofhere goes back to M.~Gromov's original paper [Invent. Math. {\bf 82} (1985), no.~2, 307--347; MR0809718]. This involvesshowing that a certain moduli space of pseudoholomorphic spheres, or aperturbation of the moduli space, has the structure of a smoothcobordism, and the novelty of the article is that this is done usingthe machinery of polyfolds, following [H.~H.~W. Hofer, K. Wysockiand 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 suitablespace ${[0,1]\times\Cal{B}}$ of maps modulo reparameterization, anM-polyfold bundle $\Cal{E}$ over $[0,1]\times\Cal{B}$, and ansc@-Fredholm section $\sigma\:[0,1]\times\Cal{B}\to\Cal{E}$ whose zeroset is the moduli space of interest. Then a general polyfoldregularization theorem is applied to perturb $\sigma$ such that itszero set is a smooth cobordism as required. The proofs should provide amodel for arguments of similar kinds requiring polyfold methods.