１－geuns 1-bridge splittings of 3-manifolds with knots
- 주제(키워드) Heegaard splitting
- 발행기관 고려대학교 대학원
- 지도교수 홍성복
- 발행년도 2010
- 학위수여년월 2010. 2
- 학위구분 박사
- 학과 일반대학원 수학과
- 세부전공 위상전공
- 원문페이지 42 p
- 실제URI http://www.dcollection.net/handler/korea/000000021402
- 본문언어 영어
- 제출원본 000045592432
초록/요약
Bonahon showed that every two Heegaard splittings of a lens space are isotopic. In the first part of this thesis, we will generalize Bonahon's result to (1,1)-splittings in 3-manifold on the condition that two (1,1)-splitting tori have a satellite diagram of a longitudinal slope,two (1,1)-splitting tori intersect each other in precisely two loops which are essential, and one of them gives the slope of the satellite diagram. In the second part of this thesis, we show that every bridge surface of certain types of (1,1) prime knot has the disjoint curve property. Also we determine when a bridge surface of a pretzel knot of type (-2,3,n) has the disjoint curve property.
more목차
Ⅰ Isotopies of (1,1)-splittings in 3-manifolds
1 Introduction
2 Some notions and lemmas
3 1-genus 1-bridge splittings for knots
3.1 General case
3.2 When
3.3 When consists of two essential loops
4. When are and isotopic?
Ⅱ The disjoint curve property and bridge surfaces
5 Introduction
6 Heegaard splitting
7 bridge surface
