Volume 4, issue 1 (2000)

Download this article
For printing
Recent Issues

Volume 22, 1 issue

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Kleinian groups and the complex of curves

Yair N Minsky

Geometry & Topology 4 (2000) 117–148

arXiv: math.GT/9907070


We examine the internal geometry of a Kleinian surface group and its relations to the asymptotic geometry of its ends, using the combinatorial structure of the complex of curves on the surface. Our main results give necessary conditions for the Kleinian group to have ‘bounded geometry’ (lower bounds on injectivity radius) in terms of a sequence of coefficients (subsurface projections) computed using the ending invariants of the group and the complex of curves.

These results are directly analogous to those obtained in the case of punctured-torus surface groups. In that setting the ending invariants are points in the closed unit disk and the coefficients are closely related to classical continued-fraction coefficients. The estimates obtained play an essential role in the solution of Thurston’s ending lamination conjecture in that case.

Kleinian group, ending lamination, complex of curves, pleated surface, bounded geometry, injectivity radius
Mathematical Subject Classification 2000
Primary: 30F40
Secondary: 57M50
Forward citations
Received: 16 July 1999
Revised: 9 November 1999
Accepted: 20 February 2000
Published: 29 February 2000
Proposed: David Gabai
Seconded: Jean-Pierre Otal, Walter Neumann
Yair N Minsky
Department of Mathematics
SUNY at Stony Brook
Stony Brook
New York 11794