Mathematics – Group Theory
Scientific paper
2006-02-14
Mathematics
Group Theory
Scientific paper
A remarkable result of McShane states that for a punctured torus with a complete finite volume hyperbolic metric we have \[ \sum_{\gamma} \frac{1}{e^{\ell(\gamma)}+1}={1/2} \] where $\gamma$ varies over the homotopy classes of essential simple closed curves and $\ell(\gamma)$ 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.
Kapovich Ilya
Rivin Igor
No associations
LandOfFree
On the absence of McShane-type identities for the outer space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the absence of McShane-type identities for the outer space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the absence of McShane-type identities for the outer space will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-568323