Topology Seminar: Bernardo Villarreal Herrera

In this talk I will give some relations between spaces of homomorphisms when the target group G is a real linear algebraic group, through homotopy stable decompositions of simplicial spaces. To obtain a simplicial space Hom(L,G) out of spaces of homomorphisms we think of L, a (suitable) family of finitely generated groups, as a cosimplicial group. Also, if G=U, the colimit of the unitary groups U(m), I will show when the geometric realization of Hom(L,U) has an "E-infinity-ring-space" structure.