Dehn surgery, homology and hyperbolic volume

Details Dehn surgery, homology and hyperbolic volume Dehn surgery, homology and hyperbolic volume

2005-08-11

arxiv.org/abs/math/0508208v4

Algebr. Geom. Topol. 6 (2006) 2297-2312

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 8 December 2006

Scientific paper

10.2140/agt.2006.6.2297

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 2 or 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 in M with the volumes of tubes about short closed geodesics in a sequence of hyperbolic manifolds obtained from M by Dehn surgeries on C.

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