AbstractIn this talk, first l will review the definition of singular cubic homologies of digraphs developed byGrigoryan, Jimenez and Muranov. Based on some geometric/topological consideration and someresults on the GJM's work, l will define the cellular homologies of digraphs in terms of the so-calledadmissible pairs and admissible relations. Also l will give several examples and properties of ...
AbstractMany manifolds of interest are equipped with a geometrical structure specified by a distinguished closed form. We will motivate the usefulness of considering pairs of differential forms that are linked together by a map of the distinguished form. We will show how this lead to new notions of Morse theory and flat connections, and also novel Yang-Mills type functionals. This talk is based...