Matroids and quotients of spheres
Matroids and quotients of spheres
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拟阵和球商
DOI：
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发表时间：
2002
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通讯作者：
Ed Swartz
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作者：
Ed Swartz
抽象的。对于球面的任意线性商，$X=S^{n-1}/Gamma，$其中Gamma$是初等交换p-群，存在相应的${mathbb F}_p$可表示拟阵$M_X$，它只依赖于X的等距类。当p为2或3时，这种对应关系导致了球面的线性行列式的等距类与初等交换p-群的等距类与F_p上可表示的拟阵之间的双射。拟阵不仅提供了大量关于商空间的几何和拓扑的信息，而且商空间的拓扑指向对一些熟悉的拟阵不变量的新见解。这些包括克拉波-罗塔临界问题不等式$chi（M;p^k）ge 0，$的推广和$mu（M）$与拟阵是否仿射之间的意想不到的关系。
Abstract. For any linear quotient of a sphere, $X=S^{n-1}/Gamma,$ where $Gamma$ is an elementary abelian p–group, there is a corresponding ${mathbb F}_p$ representable matroid $M_X$ which only depends on the isometry class of X. When p is 2 or 3 this correspondence induces a bijection between isometry classes of linear quotients of spheres by elementary abelian p–groups, and matroids representable over $F_p.$ Not only do the matroids give a great deal of information about the geometry and topology of the quotient spaces, but the topology of the quotient spaces point to new insights into some familiar matroid invariants. These include a generalization of the Crapo–Rota critical problem inequality $chi(M;p^k)ge 0,$ and an unexpected relationship between $mu(M)$ and whether or not the matroid is affine.