Speaker:  Marta Pavelka, U Miami

Title:  2-LC triangulated manifolds are exponentially many

Abstract:

We introduce "t-LC triangulated manifolds" as those triangulations obtainable from a tree of d-simplices by recursively identifying two boundary (d-1)-faces whose intersection has dimension at least d - t - 1. The t-LC notion interpolates between the class of LC manifolds introduced by Durhuus-Jonsson (corresponding to the case t = 1), and the class of all manifolds (case t = d). Benedetti-Ziegler proved that there are at most 2^(N d^2) triangulated 1-LC d-manifolds with N facets. Here we show that there are at most 2^(N/2 d^3) triangulated 2-LC d-manifolds with N facets.

We also introduce "t-constructible complexes", interpolating between constructible complexes (the case t = 1) and all complexes (case t = d). We show that all t-constructible pseudomanifolds are t-LC, and that all t-constructible complexes have (homotopical) depth larger than d - t. This extends the famous result by Hochster that constructible complexes are (homotopy) Cohen-Macaulay.

This is joint work with Bruno Benedetti. Details of the proofs and more can be found in our paper of the same title.

Marta Pavelka is a student of Bruno Benedetti.