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The Number of Four Dimensional PL-spheres with Nine Vertices
- Author(s)
- 장현태
- Advisor
- 최수영
- Department
- 일반대학원 수학과
- Publisher
- The Graduate School, Ajou University
- Publication Year
- 2020-08
- Language
- eng
- Alternative Abstract
- 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.
- Fulltext
- Appears in Collections:
- Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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