Sesión Geometría, Topología y Teoría de LieColimits of A-spaces and weak cores
Juan Galotto
Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Matemática, Argentina - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
Alexandroff spaces (or A-spaces) are topological spaces in which arbitrary intersections of open sets are open. Every topological space is weak homotopy equivalent to an A-space by a result of McCord. An important class of A-spaces is given by finite spaces. The core of a finite space \(X\) is a space \(Y\) such that there is a quotient map \(X \xrightarrow{q} Y\) which is a homotopy equivalence, and where \(Y\) is minimal with this property.
In this talk, we will study filtered colimits of A-spaces, and we will prove that although A-spaces do not have cores in general, they do possess weak cores: a version in which homotopy equivalences are replaced by weak equivalences.
If time allows, we will also study colimits of CW-complexes which are A-spaces.
Trabajo en conjunto con: Jonathan Barmak (Universidad de Buenos Aires)..
Referencias
[1] J.A. Barmak, J.I. Galotto. Directed systems and weak cores of A-spaces. 2026.