2013 Fiscal Year Final Research Report
A ring theoretic approach to face numbers of triangulated manifolds
| Project/Area Number |
22740018
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Yamaguchi University |
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Principal Investigator |
MURAI Satoshi 山口大学, 理工学研究科, 准教授 (90570804)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | f-列 / 単体的複体 / 単体的セル複体 / 三角形分割 |
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| Research Abstract |
The study of face vectors of simplicial complexes and simplicial cell complexes is a current trend in combinatorics. In particular, face vectors of triangulated spheres and manifolds has been of great interest in this research area. In this research project, we get the following results on this topic. (1) characterizations of face vectors of simplicial cell decompositions of products of spheres and those of balls (2) solution of the generalized lower bound conjecture for simplicial polytopes.
The second result sovles a conjecture of McMullen and Walkup in 1971.
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