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タイトル: A linear bound on the tetrahedral number of manifolds of bounded volume (after Jorgensen and Thurston)
著者: Kobayashi, Tsuyoshi link image; Rieck, Yo'av
著者(別表記) : 小林, 毅
著者読み: こばやし, つよし
発行日: 2011年
出版者: American Mathematical Society
引用: Kobayashi, Tsuyoshi and Rieck, Yo'av: Topology and geometry in dimension three, 27-42, Contemp. Math., 560, Amer. Math. Soc.
シリーズ/レポート番号: Contemporary Mathematics; Vol.560
抄録: We provide a detailed proof of the following folklore theorem: Let mu > 0 be a Margulis constant for 3-dimensional hyperbolic space. Then for any d>0 there exists a constant K>0, depending on mu and d, so that for any complete finite volume hyperbolic 3-manifold M, the d-neighborhood of the mu-thick part of M can be triangulated using at most K Vol(M) tetrahedra; here Vol is the hyperbolic volume function. As a corollary, we obtain the following topological interpretation of the volume: the minimal number of tetrahedra required to triangulate a link exterior in M is linearly equivalent to Vol(M); for a precise statement see Corollary 1.3.
記述: Final version. Pagination and numbering may differ from published version. The First Published in "Topology and geometry in dimension three : triangulations, invariants, and geometric structures : Conference in Honor of William Jaco's 70th Birthday, June 4-6, 2010, Oklahoma State University, Stillwater, Oklahoma (Contemporary Mathematics Vol.560)" in 2011, Published by American Mathematical Society. © 2011, American Mathematical Society.
URI: http://hdl.handle.net/10935/4668
ISBN: 9780821852958
出現コレクション:図書

このアイテムの引用には次の識別子を使用してください: http://hdl.handle.net/10935/4668

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