O symetrii

• Autorzy: Kędra Jarek

Identyfikatory

DOI

10.14708/wm.v44i01.5082

• Języki publikacji: PL

Abstrakty

EN

The present paper is a survey on the topology of diffeomomorphism groups of smooth manifolds. We start with a very mild introduction of the concept of symmetry. We show that symmetries of a space form a topological group. We present some classical results about the topology of diffeomorphism groups of surfaces and four dimensional symplectic manifolds. Then we survey on author’s results about the topology of symplectic diffeomorphisms, Hamiltonian actions of compact Lie groups and characteristic classes.

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Wiadomości Matematyczne
• Rocznik: 2008
• Tom: T. 44, Nr 1
• Strony: 23--33
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Kędra Jarek

• Mathematical Sciences University of Aberdeen Meston Building AB243UE Aberdeen Scotland, UK
• Instytut Matematyki Uniwersytet Szczeciński ul. Wielkopolska 15 70-451 Szczecin Poland

• https://orcid.org/0000-0002-1599-2482

Bibliografia

• [1] Miguel Abreu and Dusa Mc Duff, Topology of symplectomorphism groups of rational ruled surfaces, J. Amer. Math. Soc., 13 (2000), 971-1009.
• [2] Augustin Banyaga, The structure of classical diffeomorphism groups, Mathematics and its Applications, 400, Kluwer Academic Publishers Group, Dordrecht, (1997).
• [3] Raoul Bott and Loring W. Tu, Differential forms in algebraic topology, Graduate Texts in Mathematics, 82, Springer-Verlag, New York, (1982).
• [4] M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math., 82 (1985), 307-347.
• [5] Nikolai V. Ivanov, Mapping class groups, w Handbook of Geometric Topology, 523-633, North-Holland, Amsterdam, 2002.
• [6] Jarek Kędra and Dusa McDuff, Homotopy properties of Hamiltonian group actions, Geom. Topol., 9 (2005), 121-162.
• [7] Jarosław Kędra, Evaluation fibrations and topology of symplectomorphisms, Proc. Amer. Math. Soc., 133 (2005), 305-312.
• [8] François Lalоnde and Martin Pinsonnault, The topology of the space of symplectic balls in rational 4-manifolds, Duke Math. J., 122 (2004), 347-397.
• [9] Dusa McDuff and Dietmar Salamon, Introduction to symplectic topology, Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York, 1998.
• [10] John Milnоr, Construction of universal bundles. I, Ann. of Math., 63 (1956), 272-284.
• [11] Jürgen Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc., 120 (1960), 286-294.
• [12] G. D. Mоstоw, Strong rigidity of locally symmetric spaces, Annals of Mathematics Studies, 78 (1973).
• [13] Alexander G. Reznikоv, Characteristic classes in symplectic topology, Selecta Math. (N.S.), 3 (1997), 601-642.
• [14] Paul Seidel, On the group of symplectic automorphisms of CP^m x CP^n, w Northern California Symplectic Geometry Seminar, Amer. Math. Soc. Transl. Ser. 2,196, 237-250. Amer. Math. Soc., Providence, RI, 1999.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).