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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On topological entropy of group actions on $ S\sp 1$


Author: Nobuya Watanabe
Journal: Proc. Amer. Math. Soc. 106 (1989), 245-249
MSC: Primary 58F11; Secondary 57S25, 58F18
DOI: https://doi.org/10.1090/S0002-9939-1989-0965946-X
MathSciNet review: 965946
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Abstract: In this paper, we show that a surface group action on $ {S^1}$ with a non-zero Euler number has a positive topological entropy. We also show that if a surface group action on $ {S^1}$ has a Euler number which attains the maximal absolute value in the inequality of Milnor-Wood, then the topological entropy of the action equals the exponential growth rate of the group.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0965946-X
Keywords: Topological entropy, surface group action, Euler number
Article copyright: © Copyright 1989 American Mathematical Society