Verified Computations for Hyperbolic 3-Manifolds

被引：22

作者：

Hoffman, Neil ^{[1
]}

Ichihara, Kazuhiro ^{[2
]}

Kashiwagi, Masahide ^{[3
]}

Masai, Hidetoshi ^{[4
]}

Oishi, Shin'ichi ^{[3
]}

Takayasu, Akitoshi ^{[3
]}

机构：

[1] Univ Melbourne, Sch Math & Stat, Parkville, Vic 3010, Australia

[2] Nihon Univ, Coll Humanities & Sci, Tokyo, Japan

[3] Waseda Univ, Dept Appl Math, Tokyo, Japan

[4] Univ Tokyo, Grad Sch Math Sci, Tokyo, Japan

来源：

EXPERIMENTAL MATHEMATICS | 2016年 / 25卷 / 01期

基金：

澳大利亚研究理事会;

关键词：

hyperbolic; 3-manifold; interval arithmetic; Krawczyk's test; verified numerical computations;

D O I：

10.1080/10586458.2015.1029599

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a given cusped 3-manifold M admitting an ideal triangulation, we describe a method to rigorously prove that either M or a filling of M admits a complete hyperbolic structure via verified computer calculations. Central to our method is an implementation of interval arithmetic and Krawczyk's test. These techniques represent an improvement over existing algorithms as they are faster while accounting for error accumulation in a more direct and user-friendly way.

引用

页码：66 / 78

页数：13

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