论文标题
紧凑型表面上梯度矢量场空间的组合结构
Combinatorial structures of the space of gradient vector fields on compact surfaces
论文作者
论文摘要
从理论和实用的角度来看，梯度流是基本对象之一。例如，各种现象被建模为梯度流。另一方面，关于梯度流动空间的拓扑知之甚少。例如，甚至还不知道梯度流的空间是否具有无连接的连接组件。在本文中，为了描述具有或没有限制条件的表面上梯度流的一般时间演变的基础，我们研究了在创造的不存在和奇异点的灭绝下，这些流动空间的拓扑。实际上，梯度流的空间具有不可收集的连接组件。
A gradient flow is one of the fundamental objects from a theoretical and practical point of view. For instance, various phenomena are modeled as gradient flows. On the other hand, little is known about the topology of the space of gradient flows. For instance, it is not even known whether the space of gradient flows has non-simply-connected connected components. In this paper, to construct a foundation for describing the possible generic time evolution of gradient flows on surfaces with or without restriction conditions, we study the topology of the space of such flows under the non-existence of creations and annihilations of singular points. In fact, the space of gradient flows has non-contractible connected components.
