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Average Genus of Oriented Rational Links
Title
Average Genus of Oriented Rational Links
Author
Ray, Dawn
Date Created
2022
Subjects--Topical
Mathematics
Description
The goal of this dissertation is to develop the formulation of the average minimal genus of all reduced alternating rational links with a given crossing number. Work has been done by N. Dunfield to approximate the growth of the genus of knots with...
Braid Indices in a Class of Closed Braids
Title
Braid Indices in a Class of Closed Braids
Author
Hinson, Kenneth
Date Created
2010
Description
A long-standing problem in knot theory concerns the additivity of crossing numbers of links under the connected sum operation. It is conjectured that if L1 and L2 are links, then Cr(L1#L2)=Cr(L1)+Cr(L2), but so far this has been proved only for ce...
Braid Indices in a Class of Closed Braids
Title
Braid Indices in a Class of Closed Braids
Author
Hinson, Kenneth
Date Created
2010
Subjects--Topical
Mathematics
Description
A long-standing problem in knot theory concerns the additivity of crossing numbers of links under the connected sum operation. It is conjectured that if L1 and L2 are links, then Cr(L1#L2)=Cr(L1)+Cr(L2), but so far this has been proved only for ce...
THE BRAID INDICES OF ALTERNATING LINKS
Title
THE BRAID INDICES OF ALTERNATING LINKS
Author
Liu, Pengyu
Date Created
2018
Description
It is well known in knot theory that any link can be represented by a closed braid and the braid index of a link is the invariant defined as the minimum number of strands in any closed braid representing the link. It is difficult in general to det...
THE BRAID INDICES OF ALTERNATING LINKS
Title
THE BRAID INDICES OF ALTERNATING LINKS
Author
Liu, Pengyu
Date Created
2018
Subjects--Topical
Mathematics
Description
It is well known in knot theory that any link can be represented by a closed braid and the braid index of a link is the invariant defined as the minimum number of strands in any closed braid representing the link. It is difficult in general to det...
Writhe-like Invariants of Alternating Links
Title
Writhe-like Invariants of Alternating Links
Author
Pham, Van
Date Created
2022
Subjects--Topical
Mathematics
Description
This dissertation introduces new invariants for a large class of links in knot theory, called alternating links. It also analyzes the strength of these invariants, that we call writhe-like invariants, in comparison with a few general link invarian...