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On the geodesic distance and group actions on trees

Published online by Cambridge University Press:  24 October 2008

Marco Pavone
Marco Pavone
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, 10129, Torino, Italy
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Extract

The natural distance function on the vertices of a tree is a kernel of negative type. As a corollary, for any group G acting on a tree X, the length function |g| = d(υ, gυ) is a negative definite function on G for any given vertex υ of X.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 1 , July 1991 , pp. 67 - 70
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

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