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Generic coarse geometry of leaves

Alvarez Lopez, Jesus A.

Generic coarse geometry of leaves

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Generic coarse geometry of leavesby Jesus A. Alvarez Lopez, Alberto Candel.
作者:	Alvarez Lopez, Jesus A.
其他作者:	Candel, Alberto.
出版者:	Cham :Springer International Publishing :2018.
面頁冊數:	xv, 173 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Foliations (Mathematics)
電子資源:	http://dx.doi.org/10.1007/978-3-319-94132-5
ISBN:	9783319941325$q(electronic bk.)

Generic coarse geometry of leaves
Alvarez Lopez, Jesus A.

Generic coarse geometry of leaves[electronic resource] /by Jesus A. Alvarez Lopez, Alberto Candel. - Cham :Springer International Publishing :2018. - xv, 173 p. :ill., digital ;24 cm. - Lecture notes in mathematics,22230075-8434 ;. - Lecture notes in mathematics ;2035..

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.

ISBN: 9783319941325$q(electronic bk.)

Standard No.: 10.1007/978-3-319-94132-5doiSubjects--Topical Terms:

340148
Foliations (Mathematics)

LC Class. No.: QA613.62 / .A483 2018

Dewey Class. No.: 514.72

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520 $a 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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