On the uniform perfectness of equivariant diffeomorphism groups for principal g manifolds

• Autorzy: Fukui K.

Identyfikatory

DOI

10.7494/OpMath.2017.37.3.381

• Języki publikacji: EN

Abstrakty

EN

We proved in [K. Abe, K. Fukui, On commutators of equivariant diffeomorphisms, Proc. Japan Acad. 54 (1978), 52–54] that the identity component [formula] of the group of equivariant Cr-diffeomorphisms of a principal G bundle M over a manifold B is perfect for a compact connected Lie group G and [formula] In this paper, we study the uniform perfectness of the group of equivariant Cr-diffeomorphisms for a principal G bundle M over a manifold B by relating it to the uniform perfectness of the group of Cr-diffeomorphisms of B and show that under a certain condition, [formula] is uniformly perfect if B belongs to a certain wide class of manifolds. We characterize the uniform perfectness of the group of equivariant Cr-diffeomorphisms for principal G bundles over closed manifolds of dimension less than or equal to 3, and in particular we prove the uniform perfectness of the group for the 3-dimensional case and r ≠ 4.

Słowa kluczowe

EN

uniform perfectness; principal G manifold; equivariant diffeomorphism

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2017
• Tom: Vol. 37, no. 3
• Strony: 381--388
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Fukui K.

• Kyoto Sangyo University Department of Mathematics Kyoto 603-8555, Japan

Bibliografia

• [1] K. Abe, K. Fukui, On commutators of equivariant diffeomorphisms, Proc. Japan Acad.54 (1978), 52–54.
• [2] K. Abe, K. Fukui, Erratum and addendum to “Commutators of C1-diffeomorphismspreserving a submanifold”, J. Math. Soc. Japan 65 (2013) 4, 1–8.
• [3] A. Banyaga, The Structure of Classical Diffeomorphisms, Kluwer Akademic Publisher,Dordrecht, 1997.
• [4] D. Burago, S. Ivanov, L. Polterovich, Conjugation-invariant norms on groups of geometricorigin, Advanced Studies in Pure Math. 52, Groups of Diffeomorphisms (2008),221–250.
• [5] W.D. Curtis, The automorphism group of a compact group action, Trans. Amer. Math.Soc. 203 (1975), 45–54.388 Kazuhiko Fukui
• [6] K. Fukui, Commutator length of leaf preserving diffeomorphisms, Publ. Res. Inst. Math.Sci. Kyoto Univ. 48 (2012) 3, 615–622.
• [7] J.M. Gambaudo, É. Ghys, Commutators and diffeomorphisms of surfaces, Ergod. Th.& Dynam. Sys. 24 (1980) 5, 1591–1617.[8] J.N. Mather, Commutators of diffeomorphisms I and II, Comment. Math. Helv. 49(1974), 512–528; 50 (1975), 33–40.
• [9] W. Thurston, Foliations and groups of diffeomorphisms, Bull. Amer. Math. Soc. 80(1974), 304–307.
• [10] T. Tsuboi, On the uniform perfectness of diffeomorphism groups, Advanced Studies inPure Math. 52, Groups of Diffeomorphisms (2008), 505–524.
• [11] T. Tsuboi, On the uniform perfectness of the groups of diffeomorphisms ofeven-dimensional manifolds, Comment. Math. Helv. 87 (2012), 141–185.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).