arXiv Analytics

Sign in

arXiv:0806.1188 [math.GT]AbstractReferencesReviewsResources

Four-free groups and hyperbolic geometry

Marc Culler, Peter B. Shalen

Published 2008-06-06, updated 2020-11-02Version 4

We give new information about the geometry of closed, orientable hyperbolic 3-manifolds with 4-free fundamental group. As an application we show that such a manifold has volume greater than 3.44. This is in turn used to show that if M is a closed orientable hyperbolic 3-manifold such that vol M < 3.44, then H_1(M;Z/2Z) has dimension at most 7.

Comments: 64 pages, 4 figures. This version corrects an error in the third paragraph of the proof of Lemma 13.3
Journal: J. Topol. 5 (2012), no. 1, 81-136
Categories: math.GT
Subjects: 57M50
Related articles: Most relevant | Search more
arXiv:math/0503163 [math.GT] (Published 2005-03-08, updated 2009-04-12)
The rank of the fundamental group of certain hyperbolic 3-manifolds fibering over the circle
arXiv:1101.1162 [math.GT] (Published 2011-01-06, updated 2011-10-27)
Three manifold groups, Kaehler groups and complex surfaces
arXiv:0904.0237 [math.GT] (Published 2009-04-01)
Geometry, Heegaard splittings and rank of the fundamental group of hyperbolic 3-manifolds

Links

Toolbox