Discrete Morse Theory and Extended L 2 Homology
نویسندگان
چکیده
منابع مشابه
Discrete Morse theory and extendedL2 homology
A brief overviewof Forman’s discrete Morse theory is presented, from which analogues of the main results of classical Morse theory can be derived for discrete Morse functions, these being functions mapping the set of cells of a CW complex to the real numbers satisfying some combinatorial relations. The discrete analogue of the strong Morse inequality was proved by Forman for finite CW complexes...
متن کاملComputing Persistent Homology via Discrete Morse Theory
This report provides theoretical justification for the use of discrete Morse theory for the computation of homology and persistent homology, an overview of the state of the art for the computation of discrete Morse matchings and motivation for an interest in these computations, particularly from the point of view of topological data analysis. Additionally, a new simulated annealing based method...
متن کاملEquivariant discrete Morse theory
In this paper, we study Forman's discrete Morse theory in the case where a group acts on the underlying complex. We generalize the notion of a Morse matching, and obtain a theory that can be used to simplify the description of the G-homotopy type of a simplicial complex. As an application, we determine the C2 × Sn−2-homotopy type of the complex of non-connected graphs on n nodes.
متن کاملDiscrete Morse Theory and Localization
Incidence relations among the cells of a regular CW complex produce a 2category of entrance paths whose classifying space is homotopy-equivalent to that complex. We show here that each acyclic partial matching on (the cells of) such a complex corresponds precisely to a homotopy-preserving localization of the associated entrance path category. Restricting attention further to the full localized ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1999
ISSN: 0022-1236
DOI: 10.1006/jfan.1999.3439