1 research outputs found
Super efficiency of efficient geodesics in the complex of curves
We show that efficient geodesics have the strong property of "super
efficiency". For any two vertices, , in the complex
of curves of a closed oriented surface of genus , and any efficient
geodesic, , it was previously established
by Birman, Margalit and the second author (see arXiv:1408.4133) that there is
an explicitly computable list of at most candidates for
the vertex. In this note we establish a bound for this computable list
that is independent of -distance and only dependent on genus---the
super efficiency property. The proof relies on a new intersection growth
inequality between intersection number of curves and their distance in the
complex of curves, together with a thorough analysis of the dot graph
associated with the intersection sequence.Comment: 24 pages, 20 figure