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Biperiodic Knots.

Guilbault, Kelvin.

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Biperiodic Knots.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Biperiodic Knots./
Author:	Guilbault, Kelvin.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
Description:	106 p.
Notes:	Source: Dissertations Abstracts International, Volume: 83-04, Section: B.
Contained By:	Dissertations Abstracts International83-04B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28717980
ISBN:	9798538153046

Biperiodic Knots.
Guilbault, Kelvin.

Biperiodic Knots. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 106 p.

Source: Dissertations Abstracts International, Volume: 83-04, Section: B.

Thesis (Ph.D.)--Indiana University, 2021.

This thesis investigates knots which are symmetric with respect to an action by a product of finite cyclic groups. Define a knot K to be (m,n)-biperiodic if there is a group action Zm x Zn on S3 leaving K invariant such that Zm x 1 and 1 x Zn have circular fixed sets which combine to form a Hopf link, disjoint from K. The (m, n)-torus knot is an example of an (m,n)-biperiodic knot.The main result adapts an equation discovered by Murasugi on the Alexander polynomials of periodic knots to the biperiodic context, showing that the Alexander polynomial of an (m, n)-biperiodic knot must factor in a particular way. We conclude by discussing to what extent Murasugi's equation and its biperiodic counterpart characterize the Alexander polynomials of periodic and biperiodic knots respectively.Building upon work by Davis-Livingston in the periodic context, we identify a class of knot polynomials always realized as Alexander polynomials of biperiodic knots. Then in the periodic context, we identify a knot polynomial satisfying Murasugi's equation which cannot be realized by a periodic knot, answering a conjecture by Davis-Livingston.

ISBN: 9798538153046Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Geometric Topology

Biperiodic Knots.
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020 $a 9798538153046
035 $a (MiAaPQ)AAI28717980
035 $a AAI28717980
040 $a MiAaPQ $c MiAaPQ
100 1 $a Guilbault, Kelvin. $3 3769846
245 1 0 $a Biperiodic Knots.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2021
300 $a 106 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-04, Section: B.
500 $a Advisor: Davis, James.
502 $a Thesis (Ph.D.)--Indiana University, 2021.
520 $a This thesis investigates knots which are symmetric with respect to an action by a product of finite cyclic groups. Define a knot K to be (m,n)-biperiodic if there is a group action Zm x Zn on S3 leaving K invariant such that Zm x 1 and 1 x Zn have circular fixed sets which combine to form a Hopf link, disjoint from K. The (m, n)-torus knot is an example of an (m,n)-biperiodic knot.The main result adapts an equation discovered by Murasugi on the Alexander polynomials of periodic knots to the biperiodic context, showing that the Alexander polynomial of an (m, n)-biperiodic knot must factor in a particular way. We conclude by discussing to what extent Murasugi's equation and its biperiodic counterpart characterize the Alexander polynomials of periodic and biperiodic knots respectively.Building upon work by Davis-Livingston in the periodic context, we identify a class of knot polynomials always realized as Alexander polynomials of biperiodic knots. Then in the periodic context, we identify a knot polynomial satisfying Murasugi's equation which cannot be realized by a periodic knot, answering a conjecture by Davis-Livingston.
590 $a School code: 0093.
650 4 $a Mathematics. $3 515831
650 4 $a Algebra. $3 516203
650 4 $a Polynomials. $3 604754
650 4 $a Neighborhoods. $3 993475
650 4 $a Knots. $3 3686077
653 $a Geometric Topology
653 $a Knot Theory
653 $a Topology
690 $a 0405
710 2 $a Indiana University. $b Mathematics. $3 1036206
773 0 $t Dissertations Abstracts International $g 83-04B.
790 $a 0093
791 $a Ph.D.
792 $a 2021
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28717980