On a Universal Mapping Class Group of Genus Zero
On a Universal Mapping Class Group of Genus Zero
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论零属的通用映射类群
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
C. Kapoudjian
中科院分区：
文献类型：
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作者：
L. Funar;C. Kapoudjian
摘要：本文的目的是引入一个包含所有亏格零曲面的映射类群的群。粗略地说，这样的群旨在成为圆的微分同胚群的离散类似物。确实定义了属零的通用映射类群，表示为
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$$mathcal{B}.$$ 后者是 Thompson 群 V（作用于康托集）的非平凡扩展，通过所有属零曲面的纯映射类群的归纳极限。我们证明
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$$mathcal{B}$$ 是一个有限呈现群，并给出它的显式呈现。
Abstract.The aim of this paper is to introduce a group containing the mapping class groups of all genus zero surfaces. Roughly speaking, such a group is intended to be a discrete analogue of the diffeomorphism group of the circle. One defines indeed a universal mapping class group of genus zero, denoted
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$$mathcal{B}.$$ The latter is a nontrivial extension of the Thompson group V (acting on the Cantor set) by an inductive limit of pure mapping class groups of all genus zero surfaces. We prove that
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$$mathcal{B}$$ is a finitely presented group, and give an explicit presentation of it.