Classical homology of a topological space provides invariants of the space by means of triangulation or squaring made up from singular simplices (simplicial homology) or singular cubes (cubical homology) in the space. In much the same way, Mazzola's hypergestural homology intends to associate invariants to topological categories and, in particular, topological spaces by means of approximation with hypergestures playing the role of singular simplices and singular cubes. In this article, we locate Mazzola's hypergestural homology as a special kind of abstract cubical homology and propose two variations of Mazzola's construction, corresponding to simple geometric and physical interpretations of boundaries of hypergestures. Moreover, we discuss the relationship between hypergestural homology and classical cubical homology and prove that in many cases, one of our hypergestural homologies is invariant under homotopy equivalence of spaces, which is the main result of the article. Also, based on some examples, several structural improvements of hypergestural homology are suggested. However, one of these examples suggests that hypergestural homology could provide combinatorial information about a topological space beyond classical homology. Our computations are based on an explicit presentation of hypergestures, not included in previous works on gesture theory. This article has an Online Supplement, in which we expose some technical details, including the proof of the main result.

拓扑空间的经典同源性是通过三角或由空间中的奇异单纯形（简单同源性）或奇异立方体（立方相似性）组成的平方来提供空间的不变性。Mazzola的超姿势同源性旨在以与超姿势近似的方式将不变量与拓扑类别（尤其是拓扑空间）相关联扮演奇异的简单体和奇异的立方体的角色。在本文中，我们将Mazzola的超姿势同源性定位为一种特殊的抽象立方同源性，并提出了Mazzola构造的两个变体，分别对应于对超姿势边界的简单几何和物理解释。此外，我们讨论了超姿势同源性和经典立方同源性之间的关系，并证明在许多情况下，同态对等下我们的一种超姿势同源性是不变的空格，这是本文的主要结果。而且，基于一些例子，提出了几种改善手势同源性的结构。但是，这些示例之一表明，超级手势同源性可以提供有关经典同源性以外的拓扑空间的组合信息。我们的计算基于手势的显式表示，而以前有关手势理论的著作中未包含这些手势。本文有一个在线补充，其中我们提供了一些技术细节，包括主要结果的证明。