On topological entropy of group actions on s

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Abstract

In this paper, we show that a surface group action on s1 with a non-zero Euler number has a positive topological entropy. We also show that if a surface group action on Sl 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.

Original languageEnglish
Pages (from-to)245-249
Number of pages5
JournalProceedings of the American Mathematical Society
Volume106
Issue number1
DOIs
Publication statusPublished - 1989

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Keywords

  • Euler number
  • Surface group action
  • Topological entropy

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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