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The Geometry of Carrier Graphs in Hy...

Siler, William Michael.

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The Geometry of Carrier Graphs in Hyperbolic 3-Manifolds.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The Geometry of Carrier Graphs in Hyperbolic 3-Manifolds./
作者:	Siler, William Michael.
面頁冊數:	46 p.
附註:	Source: Dissertation Abstracts International, Volume: 74-12(E), Section: B.
Contained By:	Dissertation Abstracts International74-12B(E).
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3573388
ISBN:	9781303435638

The Geometry of Carrier Graphs in Hyperbolic 3-Manifolds.
Siler, William Michael.

The Geometry of Carrier Graphs in Hyperbolic 3-Manifolds. - 46 p.

Source: Dissertation Abstracts International, Volume: 74-12(E), Section: B.

Thesis (Ph.D.)--University of Illinois at Chicago, 2013.

A carrier graph is a map from a finite graph to a hyperbolic 3-manifold M, which is surjective on the level of fundamental groups. We can pull back the metric on M to get a notion of length for the graph. We study the geometric properties of the carrier graphs with minimal possible length. We show that minimal length carrier graphs exist for a large class of 3-manifolds. We also show that those manifolds have only finitely many minimal length carrier graphs, from which we deduce a new proof that such manifolds have finite isometry groups. Finally, we give a theorem relating lengths of loops in a minimal length carrier graph to the lengths of its edges. From this we are able, for example, to get an explicit upper bound on the injectivity radius of M based on the lengths of edges in a minimal length carrier graph. vii.

ISBN: 9781303435638Subjects--Topical Terms:

515831
Mathematics.

The Geometry of Carrier Graphs in Hyperbolic 3-Manifolds.
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500 $a Adviser: Peter Shalen.
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520 $a A carrier graph is a map from a finite graph to a hyperbolic 3-manifold M, which is surjective on the level of fundamental groups. We can pull back the metric on M to get a notion of length for the graph. We study the geometric properties of the carrier graphs with minimal possible length. We show that minimal length carrier graphs exist for a large class of 3-manifolds. We also show that those manifolds have only finitely many minimal length carrier graphs, from which we deduce a new proof that such manifolds have finite isometry groups. Finally, we give a theorem relating lengths of loops in a minimal length carrier graph to the lengths of its edges. From this we are able, for example, to get an explicit upper bound on the injectivity radius of M based on the lengths of edges in a minimal length carrier graph. vii.
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