Surface subgroups from homology

Calegari, Danny¹

¹ Department of Mathematics, Caltech, Pasadena CA, 91125

Geometry & topology, Tome 12 (2008) no. 4, pp. 1995-2007.

Résumé

Let $G$ be a word-hyperbolic group, obtained as a graph of free groups amalgamated along cyclic subgroups. If $H_2\left(G;\mathbb{Q}\right)$ is nonzero, then $G$ contains a closed hyperbolic surface subgroup. Moreover, the unit ball of the Gromov–Thurston norm on $H_2\left(G;ℝ\right)$ is a finite-sided rational polyhedron.

Détail

DOI : 10.2140/gt.2008.12.1995

Keywords: hyperbolic group, surface subgroup, graph of groups, Thurston norm, rational polyhedron

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