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Examples and Open Problems

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Generic Coarse Geometry of Leaves

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2223))

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Abstract

This final chapter contains a variety of examples that serve to illustrate our main theorems, as well as a list of open problems on the topics that we have studied in this book.

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Notes

  1. 1.

    This set is well defined by assuming that the underlying set of every M is contained in a common set.

  2. 2.

    Recall that an orientation of an edge can be understood as an order of its vertices, which can be written as an ordered pair of its vertices.

  3. 3.

    A function of the radius in polar coordinates.

  4. 4.

    Be aware that the Caley graph structures of [18] are left invariant, and ours are right invariant.

  5. 5.

    They have the same derivatives of any order as the identity map at those points.

  6. 6.

    The closure of the set of points where \(f\ne \operatorname {\mathrm {id}}\).

  7. 7.

    It is defined like a usual metric, except that the infinite distance between points is possible.

  8. 8.

    The action of a Polish group on a Polish space.

  9. 9.

    The closure has nonempty interior.

  10. 10.

    The flow maps leaves to leaves.

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Authors and Affiliations

  1. Department and Institute of Mathematics, University of Santiago de Compostela, Santiago de Compostela, Spain

    Jesús A. Álvarez López

  2. Department of Mathematics, California State University, Northridge, California, USA

    Alberto Candel

Authors
  1. Jesús A. Álvarez López
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  2. Alberto Candel
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Álvarez López, J.A., Candel, A. (2018). Examples and Open Problems. In: Generic Coarse Geometry of Leaves. Lecture Notes in Mathematics, vol 2223. Springer, Cham. https://doi.org/10.1007/978-3-319-94132-5_11

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