We introduce a certain differential on the cohomology of a moment-angle complex Z(K) associated with a simplicial complex K to make the cohomology a chain complex. This leads us to define the "double (co)homology” of Z(K), which is a new combinatorial invariant of K. After briefly summarizing the theory of double (co)homology of Z(K), we discuss how it comes into the standard pipeline of the topological data analysis (TDA). This is a joint work with A. Bahri, I. Limonchenko, T. Panov and D. Stanley

Online Talk