The Number of Four Dimensional PL-spheres with Nine Vertices
- 주제(키워드) toric topology , real toric space , PL-sphere , bistellar move , lexicographic enumeration
- 발행기관 아주대학교
- 지도교수 최수영
- 발행년도 2020
- 학위수여년월 2020. 8
- 학위명 석사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/ajou/000000030337
- 본문언어 영어
- 저작권 아주대학교 논문은 저작권에 의해 보호받습니다.
초록/요약
We study the number of D-J classes on P L-spheres with a few vertices. The Picard number of a P L-sphere with m vertices of dimension n − 1 is defined as m − n. It is known that all PL-spheres with Picard numbers less than 4 are polytopal, and the number is well-known by Perles. Furthermore, the numbers of D-J classes over such PL-spheres have been computed by Choi and Park. Nevertheless, only little is known about P L-spheres with the Picard number 4. In this thesis, we focus on PL-spheres of the Picard number 4. It is known that there are 5 PL-spheres of dimension 2 as a corollary of Steinitz’s theorem, and 39 of dimension 3 by Barnette. We construct two algorithms to count 4 dimensional P L-spheres of the Picard number 4; one gives the lower bound and the other gives the upper bound. Using this, we show that there are exactly 337 P L-spheres of dimension 4 with 9 vertices. As a corollary, we show that there are exactly 15757 D-J classes over such PL-spheres.
more목차
1. Introduction 1
2. PL-spheres 2
2.1 SImple and Simplicial Polytopes 2
2.2 PL-Spheres 4
3. Real Toric Spaces 8
3.1 Real Toric Spaces 8
3.2 Dual Characteristic Maps 12
4. Enumeration of PL-Spheres 16
4.1 Bistellar Moves 16
4.2 Lexicographic Enumeration 18
References 24
Appendix A Gale Diagrams 27
