A Heegaard diagram for a 3-manifold is regarded as a pair of simplexes in the complex of
curves on a surface and a Heegaard splitting as a pair of subcomplexes generated by the …

We give a distance estimate for the disk complex. We use the distance estimate to prove that
the disk complex is Gromov hyperbolic. As another application of our techniques, we find an …

Alternate Heegaard genus bounds distance Page 1 Geometry & Topology 10 (2006) 593–617
593 Alternate Heegaard genus bounds distance MARTIN SCHARLEMANN MAGGY TOMOVA …

This book is a study of combinatorial structures of 3-mani-folds, especially Haken 3-
manifolds. Specifically, it is concerned with Heegard graphs in Haken 3-manifolds, ie, with …

Given a Heegaard splitting and an incompressible surface S and a Heegaard splitting of an
irreducible manifold, I shall use a generalization of Haken's lemma proved by Kobayashi in …

We give a description of the boundary of a complex of free factors that is analogous to E.
Klarreich's description of the boundary of a curve complex. The argument uses the geometry …

We introduce the co‐surface graph CS of a finitely generated free group F and use it to study
the geometry of hyperbolic group extensions of F. Among other things, we show that the …

These are the notes I prepared for talks at Caltech, January 2005. As they are doubtless
riddled with typos, mathematical errors, misattributions, and other mistakes please do email …

Given a countable group G splitting as a free product G= G 1∗⋯∗ G k∗ FN, we establish
classification results for subgroups of the group Out⁡(G, ℱ) of all outer automorphisms of G …

J. Hempel's definition of the distance of a Heegaard surface generalizes to a notion of
complexity for any knot that is in bridge position with respect to a Heegaard surface. Our …