國立虎尾科技大學 |

Biperiodic Knots.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Biperiodic Knots./
作者:	Guilbault, Kelvin.
面頁冊數:	1 online resource (106 pages)
附註:	Source: Dissertations Abstracts International, Volume: 83-04, Section: B.
Contained By:	Dissertations Abstracts International83-04B.
標題:	Knots. -
電子資源:	click for full text (PQDT)
ISBN:	9798538153046

Biperiodic Knots.
Guilbault, Kelvin.

Biperiodic Knots. - 1 online resource (106 pages)

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

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

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798538153046Subjects--Topical Terms:

1474028
Knots.
Subjects--Index Terms:

Geometric TopologyIndex Terms--Genre/Form:

554714
Electronic books.

Biperiodic Knots.
LDR:02328ntm a22003497 4500 001 1148126
005 20240916070006.5
006 m o d
007 cr bn ---uuuuu
008 250605s2021 xx obm 000 0 eng d
020 $a 9798538153046
035 $a (MiAaPQ)AAI28717980
035 $a AAI28717980
040 $a MiAaPQ $b eng $c MiAaPQ $d NTU
100 1 $a Guilbault, Kelvin. $3 1474027
245 1 0 $a Biperiodic Knots.
264 0 $c 2021
300 $a 1 online resource (106 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 83-04, Section: B.
500 $a Advisor: Davis, James.
502 $a Thesis (Ph.D.)--Indiana University, 2021.
504 $a Includes bibliographical references
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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Knots. $3 1474028
650 4 $a Neighborhoods. $3 888883
650 4 $a Polynomials. $3 528565
650 4 $a Algebra. $2 gtt $3 579870
650 4 $a Mathematics. $3 527692
653 $a Geometric Topology
653 $a Knot Theory
653 $a Topology
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a Indiana University. $b Mathematics. $3 1180679
710 2 $a ProQuest Information and Learning Co. $3 1178819
773 0 $t Dissertations Abstracts International $g 83-04B.
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28717980 $z click for full text (PQDT)