Diego Gonzalez-Sanchez: On an extension of the inverse limit theorem for nilspaces

Speaker: Diego Gonzalez-Sanchez

Title: On an extension of the inverse limit theorem for nilspaces

Abstract: The talk will start with a brief summary of the theory of nilspaces, its groups of translations, fibrations, the Inverse Limit Theorem for Nilspaces and we will also compare these concepts with equivalent ones in group theory. The question we are interested in is whether a translation can "conmmute" with a fibration. We will show that in general we cannot hope that this happens but we can always factorize our fibration through a nilspace where we will be able to do this. We will use this to prove a extension of the Inverse Limit Theorem where given some translations, the nilspace can be represented as an inverse limit where all the fibrations involved commute with these translations.