Francesca Tombari (8/27/21): Decomposing simplicial complexes (without losing pieces) скачать в хорошем качестве

Francesca Tombari (8/27/21): Decomposing simplicial complexes (without losing pieces)

When we decompose a simplicial complex and reassemble it, it might happen that the resulting complex has a different homotopy type from the initial one. However, it is sometimes possible to understand this change by looking at subcomplexes living in the intersection of the two decomposing pieces, the so called obstruction complexes. In this talk we will see how the homotopy type of a simplicial complex is related to the one of its decompositions. We will also give demonstrations of use of these ideas to find out the homotopy type of given Vietoris-Rips complexes. This is a joint work with Wojciech Chachólski, Martina Scolamiero and Alvin Jin.