A Hopf Algebra Model for Dwyer's Tame Homotopy Theory

Roughly speaking, a 3-connective space is tame if its homotopy groups become more divisible as its degree increases. As an analogy to Quillen’s rational homotopy theory, Dwyer showed that the homotopy theory of tame spaces is equivalent to the homotopy theory of certain dg Lie algebras over the integer. In this talk, I will first sketch a modern approach to Quillen’s rational homotopy theory. Then I will explain how one can adjust this approach to build an Hopf algebra model for tame spaces. Finally, I will explain the Hopf algebra model is equivalent to Dwyer’s Lie algebra model via a universal enveloping algebra functor.