arXiv subjects
Publications and source records attributed to F. Gautero.
We show that the problem of tiling the Euclidean plane with a finite set of polygons (up to translation) boils down to prove the existence of zeros of a non-negative convex function defined on a finite-dimensional simplex. This function is a generalisation, in the framework of branched surfaces, of the Thurston semi-norm originally defined for compact $3$-manifolds.
We present a careful approximation of the geodesics in trees of hyperbolic or relatively hyperbolic groups. As an application we prove a combination theorem for finite graphs of relatively hyperbolic groups, with both Farb's and Gromov's definitions.
We give a cohomological characterization of Gromov relative hyperbolicity. As an application we prove a converse to the combination theorem for graphs of relatively hyperbolic groups given in a previous paper of the first author. We build upon, and follow the ideas of, the work of S. Gersten in ``Cohom. lower bounds for isoperim. funct. on groups'' (Topology 37, 1998) about the same topics in the classical Gromov hyperbolic setting.