Abstract
A remarkable result of McShane states that for a punctured torus with a complete finite volume hyperbolic metric we haveunder(∑, γ) frac(1, eℓ (γ) + 1) = frac(1, 2) where γ varies over the homotopy classes of essential simple closed curves and ℓ (γ) is the length of the geodesic representative of γ. We prove that there is no reasonable analogue of McShane's identity for the Culler-Vogtmann outer space of a free group.
Original language | English (US) |
---|---|
Pages (from-to) | 3659-3670 |
Number of pages | 12 |
Journal | Journal of Algebra |
Volume | 320 |
Issue number | 10 |
DOIs | |
State | Published - Nov 15 2008 |
Keywords
- Free groups
- Outer space
ASJC Scopus subject areas
- Algebra and Number Theory