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

Ilya Kapovich, Igor Rivin

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)3659-3670
Number of pages12
JournalJournal of Algebra
Issue number10
StatePublished - Nov 15 2008


  • Free groups
  • Outer space

ASJC Scopus subject areas

  • Algebra and Number Theory


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