f-Vectors of 3-Manifolds
f-Vectors of 3-Manifolds
复制标题
3-流形的 f-向量
DOI：
10.37236/79
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Ed Swartz
中科院分区：
文献类型：
--
作者：
Frank H. Lutz;T. Sulanke;Ed Swartz
1970年，Walkup完整描述了四个3流形$S^3$、$S^2扭曲S^1$、$S^2\times S^1$和$RP^3$的$f$向量集。我们改进了 Walkup 在 3 流形 $f$ 向量集上的主要限制不等式之一。由于 Novik 和 Swartz 的界限，我们还根据其 $\beta_1$ 系数得出了组合 $d$ 流形所需顶点数量的新下界，这部分解决了 K\"uhnel 的猜想。枚举结果和对双星翻转小三角剖分的搜索使我们能够与新界限相结合，完全确定 $f$ 向量集对于另外二十个 3-流形，即球束 $(S^2 \times S^1)^{# k}$ 和扭曲球束 $(S^2 twin S^1)^{# k}$ 的连通和，其中 $k=2,3,4,5,6,7,8,10,11,14$，对于更多不同几何类型的 3-流形，我们提供小三角剖分和部分三角剖分。此外，我们表明 3 流形 $RP^3 # RP^3$ 有（至少）两个不同的最小 $g$-向量。
In 1970, Walkup completely described the set of $f$-vectors for the four 3-manifolds $S^3$, $S^2 twist S^1$, $S^2 \times S^1$, and $RP^3$. We improve one of Walkup's main restricting inequalities on the set of $f$-vectors of 3-manifolds. As a consequence of a bound by Novik and Swartz, we also derive a new lower bound on the number of vertices that are needed for a combinatorial $d$-manifold in terms of its $\beta_1$-coefficient, which partially settles a conjecture of K\"uhnel. Enumerative results and a search for small triangulations with bistellar flips allow us, in combination with the new bounds, to completely determine the set of $f$-vectors for twenty further 3-manifolds, that is, for the connected sums of sphere bundles $(S^2 \times S^1)^{# k}$ and twisted sphere bundles $(S^2 twist S^1)^{# k}$, where $k=2,3,4,5,6,7,8,10,11,14$. For many more 3-manifolds of different geometric types we provide small triangulations and a partial description of their set of $f$-vectors. Moreover, we show that the 3-manifold $RP^3 # RP^3$ has (at least) two different minimal $g$-vectors.
影响因子：
0.7
作者：
.Ilker S. Yuce-Ilker-S.-Yuce-102800584
通讯作者：
.Ilker S. Yuce-Ilker-S.-Yuce-102800584