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Fibers as Normal and Spun-Normal Sur...

Bryant, Birch.

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Fibers as Normal and Spun-Normal Surfaces in Link Manifolds.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Fibers as Normal and Spun-Normal Surfaces in Link Manifolds./
Author:	Bryant, Birch.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
Description:	76 p.
Notes:	Source: Dissertations Abstracts International, Volume: 85-02, Section: B.
Contained By:	Dissertations Abstracts International85-02B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30484666
ISBN:	9798380080521

Fibers as Normal and Spun-Normal Surfaces in Link Manifolds.
Bryant, Birch.

Fibers as Normal and Spun-Normal Surfaces in Link Manifolds. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 76 p.

Source: Dissertations Abstracts International, Volume: 85-02, Section: B.

Thesis (Ph.D.)--Oklahoma State University, 2023.

The technique of inflating ideal triangulations developed by Jaco and Rubinstein in gives a procedure starting with an ideal triangulation T∗ of the interior of a compact 3-manifold M, that constructs a triangulation TΛ of M with real boundary components. This construction is carried out in such a way that combinatorial information from T∗ persists in TΛ. Viewed as an inverse operation, crushing TΛ along the boundary of M recovers exactly T∗.We present results from joint work with Jaco and Rubinstein showing, for T∗ and TΛ, there is a bijection between the closed normal surfaces of T∗ and the closed normal surfaces of TΛ. Further corresponding surfaces are homeomorphic. Given the previous relationship for closed normal surfaces, it is natural to inquire about surfaces with boundary. That is, if a surface is normal in TΛ, is there a corresponding spun-normal surface in T∗? In general the answer is no. However, we show that an affirmative answer can be given if the normal surface in TΛ is in 'C-position.'In, Cooper Tillmann and Worden pose the question For a fibered knot complement or fibered once-cusped 3-manifold M, is there always some ideal triangulation of M such that the fiber is realized as an embedded spun-normal surface. We present an algorithm that will construct an inflated triangulation TΛ in which the fiber is a normal surface in C-position, thus in the underlying ideal triangulation the fiber is realized as a spun-normal surface; answering the question in the affirmative. Further the algorithm will find the spun-normal representation of the fiber.

ISBN: 9798380080521Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Bundle

Fibers as Normal and Spun-Normal Surfaces in Link Manifolds.
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100 1 $a Bryant, Birch. $3 3769878
245 1 0 $a Fibers as Normal and Spun-Normal Surfaces in Link Manifolds.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 76 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-02, Section: B.
500 $a Advisor: Hoffman, Neil.
502 $a Thesis (Ph.D.)--Oklahoma State University, 2023.
520 $a The technique of inflating ideal triangulations developed by Jaco and Rubinstein in gives a procedure starting with an ideal triangulation T∗ of the interior of a compact 3-manifold M, that constructs a triangulation TΛ of M with real boundary components. This construction is carried out in such a way that combinatorial information from T∗ persists in TΛ. Viewed as an inverse operation, crushing TΛ along the boundary of M recovers exactly T∗.We present results from joint work with Jaco and Rubinstein showing, for T∗ and TΛ, there is a bijection between the closed normal surfaces of T∗ and the closed normal surfaces of TΛ. Further corresponding surfaces are homeomorphic. Given the previous relationship for closed normal surfaces, it is natural to inquire about surfaces with boundary. That is, if a surface is normal in TΛ, is there a corresponding spun-normal surface in T∗? In general the answer is no. However, we show that an affirmative answer can be given if the normal surface in TΛ is in 'C-position.'In, Cooper Tillmann and Worden pose the question For a fibered knot complement or fibered once-cusped 3-manifold M, is there always some ideal triangulation of M such that the fiber is realized as an embedded spun-normal surface. We present an algorithm that will construct an inflated triangulation TΛ in which the fiber is a normal surface in C-position, thus in the underlying ideal triangulation the fiber is realized as a spun-normal surface; answering the question in the affirmative. Further the algorithm will find the spun-normal representation of the fiber.
590 $a School code: 0664.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Bundle
653 $a Fiber
653 $a knot
653 $a Link
653 $a Manifold
653 $a Topology
690 $a 0405
690 $a 0642
710 2 $a Oklahoma State University. $b Mathematics. $3 3548258
773 0 $t Dissertations Abstracts International $g 85-02B.
790 $a 0664
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30484666