Online Talk

In this talk, I'll introduce the concept of filtration of regular graphs and `simplicial graph complexes'. Then, we'll introduce `simplicial GKM orbifold complexes' and study some of their topological properties. We'll discuss a necessary conditions to confirm an invariant q-CW complex structure on a simplicial GKM orbifold complex. We'll show that a `buildable' simplicial GKM orbifold complex is equivariantly formal, and a `divisive' simplicial GKM orbifold complex is integrally equivariantly formal. We give a combinatorial description of the integral equivariant cohomology ring of certain simplicial GKM orbifold complexes.