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Angled triangulations of link comple...

Futer, David.

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Angled triangulations of link complements.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Angled triangulations of link complements./
Author:	Futer, David.
Description:	102 p.
Notes:	Source: Dissertation Abstracts International, Volume: 66-08, Section: B, page: 4256.
Contained By:	Dissertation Abstracts International66-08B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3187289
ISBN:	9780542295072

Angled triangulations of link complements.
Futer, David.

Angled triangulations of link complements. - 102 p.

Source: Dissertation Abstracts International, Volume: 66-08, Section: B, page: 4256.

Thesis (Ph.D.)--Stanford University, 2005.

The goal of this thesis is to relate the projection diagram of a knot or link in S3 to the geometry and topology of the link complement. We use the diagram of a link K to obtain a Dehn surgery description of K from a hyperbolic link L. The simple geometry of S 3\L allows us to decompose it into ideal hyperbolic polyhedra, whose dihedral angles provide a lot of combinatorial information. One consequence of this approach is a mild condition on the original diagram that ensures K is hyperbolic and all its non-trivial Dehn fillings are hyperbolike. Another, closely related, consequence is a diagrammatic lower bound on the genus of K.

ISBN: 9780542295072Subjects--Topical Terms:

515831
Mathematics.

Angled triangulations of link complements.
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020 $a 9780542295072
035 $a (UnM)AAI3187289
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040 $a UnM $c UnM
100 1 $a Futer, David. $3 1783640
245 1 0 $a Angled triangulations of link complements.
300 $a 102 p.
500 $a Source: Dissertation Abstracts International, Volume: 66-08, Section: B, page: 4256.
500 $a Adviser: Steven P. Kerckhoff.
502 $a Thesis (Ph.D.)--Stanford University, 2005.
520 $a The goal of this thesis is to relate the projection diagram of a knot or link in S3 to the geometry and topology of the link complement. We use the diagram of a link K to obtain a Dehn surgery description of K from a hyperbolic link L. The simple geometry of S 3\L allows us to decompose it into ideal hyperbolic polyhedra, whose dihedral angles provide a lot of combinatorial information. One consequence of this approach is a mild condition on the original diagram that ensures K is hyperbolic and all its non-trivial Dehn fillings are hyperbolike. Another, closely related, consequence is a diagrammatic lower bound on the genus of K.
520 $a When K is an arborescent link, we use the correspondence between the link and a weighted tree to simplify the projection diagram into a particularly nice form. This simplified diagram then allows us to subdivide the link complement into hyperbolic polyhedra and tetrahedra whose dihedral angles fit together in a consistent fashion. An angled decomposition of this type implies that K is hyperbolic and provides a robust combinatorial framework for more detailed investigations into its geometry.
590 $a School code: 0212.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 0 $a Stanford University. $3 754827
773 0 $t Dissertation Abstracts International $g 66-08B.
790 1 0 $a Kerckhoff, Steven P., $e advisor
790 $a 0212
791 $a Ph.D.
792 $a 2005
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3187289