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1 results

  • 9 - Sphere systems, standard form, and cores of products of trees

  • from Part Three - Research Articles
  • Edited by Mark Hagen, University of Bristol, Richard Webb, University of Cambridge, Henry Wilton, University of Cambridge
  • Book:
    Beyond Hyperbolicity
    Published online:
    22 June 2019
    Print publication:
    11 July 2019, pp 186-222

  • Summary

    We introduce the concept of a standard form for two embedded maximal sphere systems in the doubled handlebody, and we prove an existence and uniqueness result. In particular, we show that pairs of maximal sphere systems in the doubled handlebody (up to homeomorphism) bijectively correspond to square complexes satisfying a set of properties. This work is a variant on Hatcher's normal form.