|
This article is cited in 2 scientific papers (total in 2 papers)
Birman–Hilden bundles. II
A. V. Malyutinab a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Abstract:
We study the structure of self-homeomorphism groups of fibered manifolds. A fibered topological space is a Birman–Hilden space whenever in each isotopic pair of its fiber-preserving (taking each fiber to a fiber) self-homeomorphisms the homeomorphisms are also fiber-isotopic (isotopic through fiber-preserving homeomorphisms). We prove in particular that the Birman–Hilden class contains all compact connected locally trivial surface bundles over the circle, including nonorientable ones and those with nonempty boundary, as well as all closed orientable Haken 3-manifold bundles over the circle, including nonorientable ones.
Keywords:
fiber bundle, fibering, fiber-preserving, fiberwise, locally trivial bundle, fiber-preserving self-homeomorphism, mapping class group, isotopy, homotopy, homotopy equivalence, manifold.
Received: 03.08.2023 Revised: 27.11.2023 Accepted: 28.11.2023
Citation:
A. V. Malyutin, “Birman–Hilden bundles. II”, Sibirsk. Mat. Zh., 65:2 (2024), 358–373; Siberian Math. J., 65:2 (2024), 351–362
Linking options:
https://www.mathnet.ru/eng/smj7860 https://www.mathnet.ru/eng/smj/v65/i2/p358
|
Statistics & downloads: |
Abstract page: | 24 | References: | 8 | First page: | 4 |
|