Mather-Thurston’s theory, non abelian Poincare duality and diffeomorphism groups

Resumen: I will discuss a remarkable generalization of Mather’s theorem by Thurston that relates the identity component of diffeomorphism groups to the classifying space of Haefliger structures. The homotopy type of this classifying space plays a fundamental role in foliation theory. However, it is notoriously difficult to determine its homotopy groups. Mather-Thurston theory relates the homology of diffeomorphism groups to these homotopy groups. Hence, this h-principle type theorem has been used as the main tool to get at the homotopy groups of Haefliger spaces. We talk about generalizing Thurston's method to prove analogue of MT for other subgroups of diffeomorphism groups that was conjectured to hold. Most h-principle methods use the local statement about M=R^n to prove a statement about compact manifolds. But Thurston's method is intrinsically compactly supported method and it is suitable when the local statement for M=R^n is hard to prove. As we also shall explain Thurston's point of view on this "local to global" method implies non abelian Poincare duality.

Este seminario de investigación se reúne en línea cada dos semanas, los jueves a la 1 p.m.

Para ser incluido en la lista de distribución contactar a Bernardo Villarreal (villarreal at matem dot unam dot mx).