Orbifold Morse–Smale–Witten complexes
Orbifold Morse–Smale–Witten complexes
复制标题
Orbifold Morse-Smale-Witten 复合体
DOI：
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Hansol Hong
中科院分区：
文献类型：
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作者：
Cheol;Hansol Hong
给定有效可定向轨道折叠上的 Morse-Smale 函数，我们构建其 Morse-Smale-Witten 复合体。我们表明，必须丢弃某种类型的临界点才能正确构建复合体，并且应使用适当的权重来计算梯度流。在自索引假设下，它的同调性被证明与商空间的奇异同调性同构。对于全局商轨道[M/G]，这样的复数可以理解为M的莫尔斯复数的G不变部分，其中必须定义莫尔斯复数生成元上的G作用，包括临界点处不稳定流形的方向空间。或者，在全局商的情况下，我们针对 M 上的非不变 Morse-Smale 函数引入了 Morse-Smale-Witten 复合体上弱群作用的概念，这在同源水平上产生了真正的群作用。
Given a Morse–Smale function on an effective orientable orbifold, we construct its Morse–Smale–Witten complex. We show that critical points of a certain type have to be discarded to build a complex properly, and that gradient flows should be counted with suitable weights. Its homology is proven to be isomorphic to the singular homology of the quotient space under the self-indexing assumption. For a global quotient orbifold [M/G], such a complex can be understood as the G-invariant part of the Morse complex of M, where the G-action on generators of the Morse complex has to be defined including orientation spaces of unstable manifolds at the critical points. Alternatively in the case of global quotients, we introduce the notion of weak group actions on Morse–Smale–Witten complexes for non-invariant Morse–Smale functions on M, which give rise to genuine group actions on the level of homology.
环折上同调的莫尔斯不等式
影响因子：
0.7
作者：
Hepworth R
通讯作者：
Hepworth R