The Culler-Vogtmann Outer space (capitalized for Out) is a free group analog of the Teichmüller space of a Riemann surface. It is of importance in the study of the outer automorphism group of the free group on $n$ letters, $Out(F_n)$.

Mark Culler, Karen Vogtmann?, Moduli of graphs and automorphisms of free groups_, Inventiones Mathematicae 84 (1): 91–119 (1986) doi, MR 0830040

J. Conant, K. Vogtmann, On a theorem of Kontsevich, Algebraic and Geometric Topology 3 (2003), pp. 1167–1224 pdf

Vincent Guirardel, Dynamics of $Out(F_n)$ on the boundary of Outer space. Annales Scientifiques de l’École Normale Supérieure (4), vol. 33 (2000), no. 4, 433–465.

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