Counting triangulated d-manifolds, asymptotically
In dimension d >= 3, take n simplices, and glue their facets in an
arbitrary way. You obtain a topological space that is a pseudo-manifold,
but not always a manifold. In how many ways, asymptotically, can you do
it in order to obtain a manifold? We give partial answers to this
question, in particular we determine the superexponential growth in
dimension 3, in the special case of colored manifolds. This is work in
progress with Guillem Perarnau.