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July 2017 Critical levels and Jacobi fields in a complex of cycles
Ingrid Irmer
Osaka J. Math. 54(3): 475-497 (July 2017).


In this paper it is shown that the space of tight geodesic segments connecting any two vertices in a complex of cycles has finite, uniformly bounded dimension. The dimension is defined in terms of a discrete analogue of Jacobi fields, which are explicitly constructed and shown to give a complete description of the entire space of tight geodesics. Jacobi fields measure the extent to which geodesic stability breaks down. Unlike most finiteness properties of curve complexes, the arguments presented here do not rely on hyperbolicity, but rather on structures similar to Morse theory.


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Ingrid Irmer. "Critical levels and Jacobi fields in a complex of cycles." Osaka J. Math. 54 (3) 475 - 497, July 2017.


Published: July 2017
First available in Project Euclid: 7 August 2017

zbMATH: 06775418
MathSciNet: MR3685588

Primary: 58D19
Secondary: 55U10

Rights: Copyright © 2017 Osaka University and Osaka City University, Departments of Mathematics


Vol.54 • No. 3 • July 2017
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