### Deformation Theory Seminar

Wednesday, July 24, 2019 - 2:00pm

#### Samuel Smith

St. Joseph's University

Location

University of Pennsylvania

4N30 DRL

We give some results on the universal fibration X \to UE \to Baut_1(X) for fibrations with fibre X.  When X is an elliptic space with evenly graded rational cohomology satisfying Halperin's conjecture, we prove the universal fibration has rational sectional category equal to two.  When X has finite-dimensional rational homotopy, we give a dg Lie model for the  evaluation fibration for Baut_1(X).  We apply the latter result to the problem of realizing spaces as classifying spaces and that of iterating the classifying space functor.  This is joint work with Greg Lupton.