Lengths of edges in carrier graphs

Details Lengths of edges in carrier graphs Lengths of edges in carrier graphs

2011-05-23

arxiv.org/abs/1105.4643v2

Mathematics

Geometric Topology

13 pages, 3 figures. Generalized main theorem

Scientific paper

We show that if X is a minimal length carrier graph in a hyperbolic
3-manifold, M, then if X contains a sufficiently short edge, it must contain a
short circuit, as well. The meaning of "short" depends only on the rank of the
fundamental group of M. We also expand the class of manifolds which are known
to have minimal length carrier graphs.

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