Studies on superbridge index of knots = 매듭의 초교각지수에 관한 연구

Cited 0 time in webofscience Cited 0 time in scopus
  • Hit : 506
  • Download : 0
In this thesis we study superbridge index of knots and examine some of its properties and relations with other knot invariants. Also we calculate superbridge index for some knots. In Chapter 1 we introduce definitions, notions and terminology and investigate some relations between superbridge index and other knot invariants. In Chapter 2 we present two moves on knots which do not increase the superbridge numbers. In Chapter 3 we examine knots having odd superbridge index and show that there are only finitely many knots with superbridge index 3. Moreover, we show that the list $\{ 3_1 ,\ 4_1 ,\ 5_2 ,\ 6_1 ,\ 6_2 ,\ 6_3 ,\ 7_2 ,\ 7_3 ,\ 7_4 , \ 8_4 ,\ 8_7,\ 8_9 \}$ contains all knots with superbridge index 3. And we get a new upper bound for superbridge index related with bridge index. In chapter 4 we consider the connected sums of two knots and introduce some results about the superbridge index for composite knots. Also we study marginal knots and strongly marginal knots and propose some problems about those knots. In Chapter 5 we supply the best known estimates of the superbridge index for all prime knots up to nine crossings.
Advisors
Jin, Gyo-Taekresearcher진교택researcher
Description
한국과학기술원 : 수학전공,
Publisher
한국과학기술원
Issue Date
2003
Identifier
180992/325007 / 000985338
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학전공, 2003.2, [ v, 54 p. ]

Keywords

Strongly marginal knot; Marginal knot; Superbridge index; $(p,q)$-closure; $(p.q)$-닫힘; 강한 한계매듭; 한계매듭; 초교각지수

URI
http://hdl.handle.net/10203/41859
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=180992&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
Files in This Item
There are no files associated with this item.

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0