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Meeting ID: 611 6862 3282
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Title of the thesis:

Formality and rational homotopy theory of relative homotopy automorphisms

Link to the thesis in DiVA

Author of the thesis:

Bashar Saleh

Opponent:

Aniceto Murillo (University of Malaga)

Supervisor:

Alexander Berglund

Abstract:

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 associative algebra is formal as a dg associative algebra if and only
if it is formal as a commutative dg associative algebra. We present some
consequences of these theorems in rational homotopy theory.

In Paper II, which is coauthored with Alexander Berglund, we construct a
dg Lie algebra model for the universal cover of the classifying space of
the grouplike monoid of homotopy automorphisms of a space that fix a
subspace, so called relative homotopy automorphisms.

In Paper III, which is coautohored with Hadrien Espic, we prove that the
group of homotopy classes of relative homotopy automorphisms of a simply
connected finite CW-complex is finitely presented and that the
rationalization map from this group to its rational analogue has a
finite kernel.

In Paper IV, we study rational homological stability for the classifying
space of the monoid of homotopy automorphisms of iterated connected sums
of complex projective 3-spaces.

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Meeting ID: 611 6862 3282
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