Dehn surgery, homology and hyperbolic volume

被引：20

作者：

Agol, Ian ^{[1
]}

Culler, Marc ^{[1
]}

Shalen, Peter B. ^{[1
]}

机构：

[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

来源：

ALGEBRAIC AND GEOMETRIC TOPOLOGY | 2006年 / 6卷

关键词：

D O I：

10.2140/agt.2006.6.2297

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

If a closed, orientable hyperbolic 3-manifold M has volume at most 1.22 then H-1(M; Z(p)) has dimension at most 2 for every prime p not equal 2; 7, and H-1(M; Z(2)) and H-1(M; Z(7)) have dimension at most 3. The proof combines several deep results about hyperbolic 3-manifolds. The strategy is to compare the volume of a tube about a shortest closed geodesic C subset of M with the volumes of tubes about short closed geodesics in a sequence of hyperbolic manifolds obtained from M by Dehn surgeries on C.

引用

页码：2295 / 2310

页数：16

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