Ignasi Mundet i Riera
Ignasi Mundet i Riera (University of Barcelona) посетил Лабораторию в апреле 2018 г. по приглашению научного сотрудника лаборатории К.А. Шрамова.
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13 апреля 2018 г. Ignasi Mundet i Riera выступил на еженедельном научном семинаре лаборатории с докладом "Finite subgroups of Ham and Symp".
Аннотация: Let X be a compact symplectic manifold and let Symp(X) (resp. Ham(X)) denote the group of symplectomorphisms (resp. hamiltonian diffeomorphisms) of X. I will talk about the following results: Theorem 1: Ham (X) is Jordan. More precisely, there exists a constant C (depending only on the topology of X) such that any finite subgroup G of Ham(X) has an abelian subgroup whose index in G is at most C. Theorem 2: if b_1(X)=0 then Theorem 1 holds true replacing Ham(X) by Symp(X). Ham(X) by Symp(X) and "abelian" by "abelian or 2-step nilpotent". In the first part of the seminar I will explain the context of these results. In particular, I will talk on the Jordan property for diffeomorphism groups, putting emphasis on situations where these theorems imply that the finite transformation groups in the symplectic category are much more restricted than in the smooth category. In the second part of the seminar I will explain the main ideas in the proofs of the theorems.
13 апреля 2018 г. Ignasi Mundet i Riera выступил на еженедельном научном семинаре лаборатории с докладом "Finite subgroups of Ham and Symp".
Аннотация: Let X be a compact symplectic manifold and let Symp(X) (resp. Ham(X)) denote the group of symplectomorphisms (resp. hamiltonian diffeomorphisms) of X. I will talk about the following results: Theorem 1: Ham (X) is Jordan. More precisely, there exists a constant C (depending only on the topology of X) such that any finite subgroup G of Ham(X) has an abelian subgroup whose index in G is at most C. Theorem 2: if b_1(X)=0 then Theorem 1 holds true replacing Ham(X) by Symp(X). Ham(X) by Symp(X) and "abelian" by "abelian or 2-step nilpotent". In the first part of the seminar I will explain the context of these results. In particular, I will talk on the Jordan property for diffeomorphism groups, putting emphasis on situations where these theorems imply that the finite transformation groups in the symplectic category are much more restricted than in the smooth category. In the second part of the seminar I will explain the main ideas in the proofs of the theorems.
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