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LIFTING HOMEOMORPHISMS AND FINITE ABELIAN BRANCHED COVERS OF THE 2-SPHERE

Part of: Low-dimensional topology

Published online by Cambridge University Press:  02 June 2022

HAIMIAO CHEN Open the ORCID record for HAIMIAO CHEN [Opens in a new window]
HAIMIAO CHEN*
Affiliation:
Department of Mathematics, Beijing Technology and Business University, Beijing, PR China
*
e-mail: [email protected]
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Abstract

We completely determine finite abelian regular branched covers of the 2-sphere $S^{2}$ with the property that each homeomorphism of $S^{2}$ preserving the branching set can be lifted.

Keywords

abelian branched cover2-spherelifting homeomorphism

MSC classification

Primary: 57M12: Special coverings, e.g. branched
Secondary: 57M60: Group actions in low dimensions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 106 , Issue 3 , December 2022 , pp. 504 - 507
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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References

Atalan, F., Medetogullari, E. and Ozan, Y., ‘Liftable homeomorphisms of rank two finite abelian branched covers’, Arch. Math. 116 (2021), 37–48.10.1007/s00013-020-01501-zCrossRefGoogle Scholar
Birman, J. S. and Hilden, H. M., ‘Erratum to “Isotopies of homeomorphisms of Riemann surfaces”’, Ann. of Math. (2) 185(1) (2017), 345.10.4007/annals.2017.185.1.9CrossRefGoogle Scholar
Chen, H.-M. and Shen, H., ‘How to find G-admissible coverings of a graph?’, Linear Algebra Appl. 438(8) (2015), 3303–3320.10.1016/j.laa.2012.12.041CrossRefGoogle Scholar
Ghaswala, T. and Winarski, R. R., ‘Lifting homeomorphisms and cyclic branched covers of spheres’, Michigan Math. J. 66 (2017), 885–890.10.1307/mmj/1508810819CrossRefGoogle Scholar
Margalit, D. and Winarski, R. R., ‘Braids groups and mapping class groups: the Birman–Hilden theory’, Bull. Lond. Math. Soc. 53 (2021), 643–659.10.1112/blms.12456CrossRefGoogle Scholar