Avhandlingens titel:

Formality and homotopy automorphisms in rational homotopy theory


Bashar Saleh


Marco Manetti (Sapienza Università di Roma)


Alexander Berglund


This licentiate thesis consists of two papers treating subjects in rational homotopy theory.

In Paper I, we establish two formality conditions in characteristic zero. We prove that a dg Lie algebra is formal if and only if its universal enveloping algebra is formal. We also prove that a commutative dg algebra is formal as a dg associative algebra if and only if it is formal as a commutative dg algebra. We present some consequences of these theorems in rational homotopy theory.

In Paper II, we construct a differential graded Lie model for the universal cover of the classifying space of the grouplike monoid of homotopy automorphisms of a space that fix a subspace.