Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 793-801

CURVE GRAPHS ON SURFACES OF INFINITE TYPE

Ariadna Fossas and Hugo Parlier

École Polytechnique Fédérale de Lausanne, FSB, Section de mathématiques
Station 8 - Bâtiment MA, CH-1015 Lausanne, Switzerland; ariadna.fossastenas 'at' epfl.ch

University of Fribourg, Department of Mathematics
Chemin du Musée 23, CH-1700 Fribourg, Switzerland; hugo.parlier 'at' unifr.ch

Abstract. We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense. We show that the graphs we construct are generally connected, infinite diameter and infinite rank.

2010 Mathematics Subject Classification: Primary 57M50; Secondary 05C63, 57M15.

Key words: Curve complexes, infinite type surfaces, hyperbolic surfaces.

Reference to this article: A. Fossas and H. Parlier: Curve graphs on surfaces of infinite type. Ann. Acad. Sci. Fenn. Math. 40 (2015), 793-801.

Full document as PDF file

doi:10.5186/aasfm.2015.4049