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  1. Bog
  2. Geometri
  3. Analytisk geometri

Generic Coarse Geometry of Leaves

Af: Jesus A. Alvarez Lopez, Alberto Candel Engelsk Paperback

Generic Coarse Geometry of Leaves

Af: Jesus A. Alvarez Lopez, Alberto Candel Engelsk Paperback
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This book provides a detailed introduction to the coarse quasi-isometry of leaves of a foliated space and describes the cases where the generic leaves have the same quasi-isometric invariants.

Every leaf of a compact foliated space has an induced coarse quasi-isometry type, represented by the coarse metric defined by the length of plaque chains given by any finite foliated atlas.  When there are dense leaves either all dense leaves without holonomy are uniformly coarsely quasi-isometric to each other, or else every leaf is coarsely quasi-isometric to just meagerly many other leaves.  Moreover, if all leaves are dense, the first alternative is characterized by a condition on the leaves called coarse quasi-symmetry.  Similar results are proved for more specific coarse invariants, like growth type, asymptotic dimension, and amenability. The Higson corona of the leaves is also studied. All the results are richly illustrated with examples.

The book is primarily aimed at researchers on foliated spaces. More generally, specialists in geometric analysis, topological dynamics, or metric geometry may also benefit from it.

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This book provides a detailed introduction to the coarse quasi-isometry of leaves of a foliated space and describes the cases where the generic leaves have the same quasi-isometric invariants.

Every leaf of a compact foliated space has an induced coarse quasi-isometry type, represented by the coarse metric defined by the length of plaque chains given by any finite foliated atlas.  When there are dense leaves either all dense leaves without holonomy are uniformly coarsely quasi-isometric to each other, or else every leaf is coarsely quasi-isometric to just meagerly many other leaves.  Moreover, if all leaves are dense, the first alternative is characterized by a condition on the leaves called coarse quasi-symmetry.  Similar results are proved for more specific coarse invariants, like growth type, asymptotic dimension, and amenability. The Higson corona of the leaves is also studied. All the results are richly illustrated with examples.

The book is primarily aimed at researchers on foliated spaces. More generally, specialists in geometric analysis, topological dynamics, or metric geometry may also benefit from it.

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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 173
ISBN-13: 9783319941318
Indbinding: Paperback
Udgave:
ISBN-10: 3319941313
Kategori: Analytisk geometri
Udg. Dato: 29 jul 2018
Længde: 11mm
Bredde: 156mm
Højde: 237mm
Forlag: Springer International Publishing AG
Oplagsdato: 29 jul 2018
Forfatter(e): Jesus A. Alvarez Lopez, Alberto Candel
Forfatter(e) Jesus A. Alvarez Lopez, Alberto Candel

Kategori Analytisk geometri

ISBN-13 9783319941318

Sprog Engelsk

Indbinding Paperback

Sider 173

Udgave

Længde 11mm

Bredde 156mm

Højde 237mm

Udg. Dato 29 jul 2018

Oplagsdato 29 jul 2018

Forlag Springer International Publishing AG

Kategori sammenhænge