Zero entropy subgroups of mapping class groups

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• 作者：John Franks ; Kamlesh Parwani
• 关键词：Mapping class groups ; Entropy ; Homeomorphisms and diffeomorphisms of planes and surfaces
• 刊名：Geometriae Dedicata
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：186
• 期：1
• 页码：27-38
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Geometry;
• 出版者：Springer Netherlands
• ISSN：1572-9168
• 卷排序：186

文摘

Given a group action on a surface with a finite invariant set we investigate how the algebraic properties of the induced group of permutations of that set affects the dynamical properties of the group. Our main result shows that in many circumstances if the induced permutation group is not solvable then among the homeomorphisms in the group there must be one with a pseudo-Anosov component. We formulate this in terms of the mapping class group relative to the finite set and show the stronger result that in many circumstances (e.g. if the surface has boundary) if this mapping class group has no elements with pseudo-Anosov components then it is itself solvable.