可整除凸域上的余维-1单形

IF 2 1区数学

Geometry & Topology Pub Date : 2020-01-29 DOI:10.2140/gt.2021.25.3725

Martin D. Bobb

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引用次数: 5

摘要

在凸可整除域$\ \Omega \子集$ mathbb{R} \textrm{P}^d$中适当嵌入的简单体表现得有点像黎曼流形中的平面，所以我们称它们为平面。证明了紧商流形上的余维-$1$平面集合具有象，该象是不相交的虚$(d-1)$-环面的有限集合。如果这个虚环面集合是非空的，那么它的补集的分量就是顶点为d的凸投影流形。

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Codimension-1 simplices in divisible convex domains

Properly embedded simplices in a convex divisible domain $\Omega \subset \mathbb{R} \textrm{P}^d$ behave somewhat like flats in Riemannian manifolds, so we call them flats. We show that the set of codimension-$1$ flats has image which is a finite collection of disjoint virtual $(d-1)$-tori in the compact quotient manifold. If this collection of virtual tori is non-empty, then the components of its complement are cusped convex projective manifolds with type $d$ cusps.

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来源期刊

Geometry & Topology 数学-数学

自引率

5.00%

发文量

期刊介绍： Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.