GT Seminars with Simo S. Mthethwa and Smegnsh Demelash

Simo S. Mthethwa (University of KwaZulu-Natal)

Title: A closer look at Michael's J-spaces and the like

Abstract: In this talk, we present a general framework for constructing classes of counterexamples that distinguish between families of topological spaces associated with Michael’s J-spaces. Among other things, we shall show that the lattice of ideals of closed subsets can be used to provide a general approach to study J-spaces and the like. Furthermore, this lattice forms a compact, complete lattice that satisfies an extra property.

Smegnsh Demelash (Kotebe University of Education)

Title: Rational Homotopy Type and Nilpotency of Mapping Spaces Between Projective Spaces

Abstract: Mapping spaces between projective spaces provide an excellent setting for exploring the relationship between algebraic and topological structures in rational homotopy theory. In this talk, I will discuss how differential graded algebras and L∞-algebras can be used to model these spaces and reveal their underlying rational homotopy types. Focusing on inclusions between projective spaces, I will present explicit computations of their rational homotopy types and nilpotency indices. The results shown here show that the inclusion maps preserve rational nilpotency, illustrating how algebraic models capture subtle geometric features of mapping spaces and deepen our understanding of their homotopical complexity.

These are talks in our Geometry and Topology Seminar Series.