Michelle Bucher

Free products with amalgamation and HNN-extensions of uniformly exponential growth

We prove that, with rare exceptions, groups that are free products with amalgamation or HNN-extensions are of uniformly exponential growth.

A Dual Interpretation of the Gromov–Thurston Proof of Mostow Rigidity and Volume Rigidity for Representations of Hyperbolic Lattices

We use bounded cohomology to define a notion of volume of an \(\operatorname{SO}(n,1)\)-valued representation of a lattice \(\varGamma<\operatorname{SO}(n,1)\) and, using this tool, we give a complete proof of the volume rigidity theorem of Francaviglia and Klaff (Geom. Dedicata 117, 111–124 (2006)) in this setting. Our approach gives in particular a proof of Thurston’s version of Gromov’s proof of Mostow Rigidity (also in the non-cocompact case), which is dual to the Gromov–Thurston proof using the simplicial volume invariant.

Isometric embeddings in bounded cohomology

This paper is devoted to the construction of norm-preserving maps between bounded cohomology groups. For a graph of groups with amenable edge groups we construct an isometric embedding of the direct sum of the bounded cohomology of the vertex groups in the bounded cohomology of the fundamental group of the graph of groups. With a similar technique we prove that if (X,Y) is a pair of CW-complexes and the fundamental group of each connected component of Y is amenable, the isomorphism between the relative bounded cohomology of (X,Y) and the bounded cohomology of X in degree at least 2 is isometric. As an application we provide easy and self-contained proofs of Gromov Equivalence Theorem and of the additivity of the simplicial volume with respect to gluings along \pi_1-injective boundary components with amenable fundamental group.

The simplicial volume of 3-manifolds with boundary

We provide sharp lower bounds for the simplicial volume of compact

The norm of the Euler class

3

On the definition of bolic spaces

-manifolds in terms of the simplicial volume of their boundaries. As an application, we compute the simplicial volume of several classes of

Minimal exponential growth rates of metabelian Baumslag–Solitar groups and lamplighter groups

3

The bounded Borel class and

-manifolds, including handlebodies and products of surfaces with the interval. Our results provide the first exact computation of the simplicial volume of a compact manifold whose boundary has positive simplicial volume. We also compute the minimal number of tetrahedra in a (loose) triangulation of the product of a surface with the interval.

3

We prove that the norm of the Euler class