Wanna hear a cool thing we realized while exploring lattice polytopes, but that took us much further?
So you know how in a smooth manifold, we can think of the fundamental class by integration over the manifold; that’s just de Rham cohomology of course, and we come to think of the fundamental class as something related to volumes and measures. This beautiful picture is something very geometric, in the end, one might think.
But that is not so: beyond geometric settings, the fundamental class still has a canonical interpretation; at least this is what we propose in such a way that it agrees with geometry when geometry is present. That is the result of a new paper with Stavros Papadakis and Vasiliki Petrotou. Grab it here.
It is a first paper in a series where we generalize and recontextualize earlier results in order to understand better where they come from, provide some more insight, and understand how general we can make them. Next up is combinatorial intersection cohomology for semigroup algebras and related, so enjoy.
For a cup of coffee more 