On the absence of McShane-type identities for the outer space

JOURNAL OF ALGEBRA

卷:320

Article

Kapovich, Ilya¹  Rivin, Igor² 

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[2] Temple Univ, Dept Math, Philadelphia, PA 19122 USA

关键词: Free groups;    Outer space;   

DOI  :  10.1016/j.jalgebra.2008.08.024

来源: Elsevier

【 摘 要 】

A remarkable result of McShane states that for a punctured torus with a complete finite volume hyperbolic metric we have S-gamma 1/e(l(gamma)) + 1 = 1/2 where gamma varies over the homotopy classes of essential simple closed curves and l(gamma) is the length of the geodesic representative of gamma. We prove that there is no reasonable analogue of McShane's identity for the Culler-Vogtmann outer space of a free group. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free