论文标题
广义虚拟Polyhedra的几何形状
Geometry of generalized virtual polyhedra
论文作者
论文摘要
虚拟多面体理论的部分概括（有时以不同的名称为单位）出现在圆环歧管理论中。这些概括看起来与原始的虚拟Polyhedra理论截然不同。它们基于同义理论的简单论点，而原始理论基于对欧拉特征的整合。在本文中，我们解释了这些概括与凸体的经典理论以及原始虚拟Polyhedra理论是如何相关的。本文基本上没有任何证据：所有证明和所有细节都可以在引用的文献中找到。该论文是基于我的演讲，该演讲专门介绍了V. I. Arnold在国际微分方程和动力学系统2022（Suzdal）的国际会议上成立85周年。
Partial generalizations of virtual polyhedra theory (sometimes under different names) appeared recently in the theory of torus manifolds. These generalizations look very different from the original virtual polyhedra theory. They are based on simple arguments from homotopy theory while the original theory is based on integration over Euler characteristic. In the paper we explain how these generalizations are related to the classical theory of convex bodies and to the original virtual polyhedra theory. The paper basically contains no proofs: all proofs and all details can be found in the cited literature. The paper is based on my talk dedicated to V. I. Arnold's 85-th anniversary at the International Conference on Differential Equations and Dynamical Systems 2022 (Suzdal).
