December, 2024 Boundedness of bundle diffeomorphism groups over a circle
Kazuhiko FUKUI, Tatsuhiko YAGASAKI
Author Affiliations +
J. Math. Soc. Japan Advance Publication 1-33 (December, 2024). DOI: 10.2969/jmsj/90209020

Abstract

In this paper we study boundedness of bundle diffeomorphism groups over a circle. For a fiber bundle π:MS1 with fiber N and structure group Γ and rZ0{} we distinguish an integer k=k(π,r)Z0 and construct a function ν:Diffπr(M)0Rk. When k1, it is shown that the bundle diffeomorphism group Diffπr(M)0 is bounded and clbπdDiffπr(M)0k+3, if Diffϱ,cr(E)0 is perfect for the trivial fiber bundle ϱ:ER with fiber N and structure group Γ. On the other hand, when k=0, it is shown that ν is a unbounded quasimorphism, so that Diffπr(M)0 is unbounded and not uniformly perfect. We also describe the integer k in term of the attaching map φ for a mapping torus π:MφS1 and give some explicit examples of (un)bounded groups.

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Kazuhiko FUKUI. Tatsuhiko YAGASAKI. "Boundedness of bundle diffeomorphism groups over a circle." J. Math. Soc. Japan Advance Publication 1 - 33, December, 2024. https://doi.org/10.2969/jmsj/90209020

Information

Received: 6 September 2022; Revised: 18 February 2024; Published: December, 2024
First available in Project Euclid: 12 December 2024

Digital Object Identifier: 10.2969/jmsj/90209020

Subjects:
Primary: 57R50
Secondary: 37C05 , 57R52

Keywords: boundedness , bundle diffeomorphism , commutator length , equivariant diffeomorphism , fiber bundle , uniformly perfect

Rights: Copyright ©2024 Mathematical Society of Japan

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