In 2021, I. Limonchenko, T. Panov, J. Song and D. Stanley introduced the notion of double (co)homology of a moment angle complex Z_K associated to a simplicial complex K. If K is a triangulated n-sphere, the double cohomology of its complex behaves in a particularly interesting manner. In this talk I'll start by summarizing the double homology construction, after that, I'll present three results: A computation of HH for a large class of simplicial complexes two results about the effects on HH of certain operations on triangulated spheres.

Online Talk