Đề tài " Geometrization of 3dimensional orbifolds "

Chia sẻ: Nguyen Nhi | Ngày: | Loại File: PDF | Số trang:97

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This paper is devoted to the proof of the orbifold theorem: If O is a compact connected orientable irreducible and topologically atoroidal 3-orbifold with nonempty ramiﬁcation locus, then O is geometric (i.e. has a metric of constant curvature or is Seifert ﬁbred). As a corollary, any smooth orientationpreserving nonfree ﬁnite group action on S 3 is conjugate to an orthogonal action. Contents 1. Introduction 2. 3-dimensional orbifolds 2.1. Basic deﬁnitions 2.2. Spherical and toric decompositions 2.3. Finite group actions on spheres with ﬁxed points 2.4. Proof of the orbifold theorem from the main theorem 3. ...

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