Educació artística, aprenentatges i infància. Una recerca sobre la comprensió crítica i la pràctica de l'art als museus i les escoles

We study the structure of topological groups and their classifying spaces, particularly their local properties, by means of homotopy theoretic methods. Recently, Broto-Levi-Oliver defined the concept of p-local finite group, as an algebraic object modelled on local properties of finite groups. A classifying space is attached to any p-local finite group, thus allowing us to study them from both points of view, algebraic and geometric. This concept opens the door to a new approach to the local homotopy theory of compact Lie groups and finite loop spaces. Out of it, we can expect a generalized theory that includes models for compact Lie groups and finite loop spaces with no restriction on the group of components as well as p-compact groups.This project will take care of the further development of the theory of p-local finite groups, with special attention to problems related to their classification (which is important for its relation with the classification theorem for finite simple groups or with block theory), the existence and description of exotic examples and their representation theory.Secondly, we will consider the generalisation of the theory to a theory that merge both p-local finite groups and p-compact groups, and finally we will study the implications of these results and the techniques involved in the structure of non-compact topological groups, including infinite discrete groups, Kac-Moody groups and the mapping class group and related groups