In the context of discrete Morse theory, we introduce Morse frames, which are maps that associate a set of critical simplexes to all simplexes. The main example of Morse frames are the Morse references. In particular, these Morse references allow computing Morse complexes, an important tool for homology. We highlight the link between Morse references and gradient flows. We also propose a novel presentation of the Annotation algorithm for persistent cohomology, as a variant of a Morse frame. Finally, we propose another construction, that takes advantage of the Morse reference for computing the Betti numbers in mod 2 arithmetic.

翻译：在离散莫尔斯理论的背景下，我们引入了莫尔斯框架，这是一种将临界单形关联到所有单形的映射。莫尔斯框架的主要实例是莫尔斯参考系。特别地，这些莫尔斯参考系允许计算莫尔斯复形——同调论中的重要工具。我们强调了莫尔斯参考系与梯度流之间的联系。此外，我们提出了一种新的持续上同调标注算法的表示方法，作为莫尔斯框架的一个变体。最后，我们提出另一种构造，利用莫尔斯参考系在模2算术下计算贝蒂数。