A combinatorial computation of the first Pontryagin class of the complex projective plane
A combinatorial computation of the first Pontryagin class of the complex projective plane
复制标题
复射影平面第一类庞特里亚金的组合计算
DOI：
10.1007/bf01264030
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发表时间：
1987
影响因子：
0.5
通讯作者：
L. Milin
中科院分区：
文献类型：
--
作者：
L. Milin
本文利用Wolfgang Kühnel发现的九顶点三角剖分，对复射影平面的第一庞特里亚金类的Gabrielov，Gel'fand和Losik的组合公式进行了显式计算.原公式的条件必须修改，因为每个顶点的3-球面链接的8-顶点三角剖分不能实现为4-空间中的凸多面体的面的复合体，但它可以实现为星形多面体，并且所有这些实现的空间是不连通的。
This paper carries out an explicit computation of the combinatorial formula of Gabrielov, Gel'fand, and Losik for the first Pontryagin class of the complex projective plane with the 9-vertex triangulation discovered by Wolfgang Kühnel. The conditions of the original formula must be modified since the 8-vertex triangulation of the 3-sphere link of each vertex cannot be realized as the complex of faces of a convex polytope in 4-space, but it can be so realized by a star-shaped polytope, and the space of all such realizations is not connected.