论文标题
正弯曲，圆环对称和矩形
Positive curvature, torus symmetry, and matroids
论文作者
论文摘要
我们确定了常规的矩形和圆环表示之间的联系，其各向异性组具有奇数成分。我们采用西摩（Seymour）1980年对以前的对象的分类，获得了后者的分类。此外，我们证明了最佳的常规矩阵的最佳上限至等级为9，并且我们将其应用于证明圆圈的定点圆圈的存在，该圆圈在圆环表示中具有较大的尺寸，而该属性的counders counders counders coundens cogirs cogirs cogirs cogirs cogirs cogirthe cogirthe则具有较大的圆圈。最后，我们将这些结果应用于证明具有正截面曲率和圆环对称性的Riemannian指标的新障碍。
We identify a link between regular matroids and torus representations all of whose isotropy groups have an odd number of components. Applying Seymour's 1980 classification of the former objects, we obtain a classification of the latter. In addition, we prove optimal upper bounds for the cogirth of regular matroids up to rank nine, and we apply this to prove the existence of fixed-point sets of circles with large dimension in a torus representation with this property up to rank nine. Finally, we apply these results to prove new obstructions to the existence of Riemannian metrics with positive sectional curvature and torus symmetry.
