O Professor Joseph Neisendorfer, da University of Rochester, USA, leccionará um curso breve sobre Teoria da Localização na Universidade do Minho, Braga. O curso decorrerá nos dias 18, 20, 25 e 27 de Outubro, na sala MICA (Departamento de Matemática, Ala Antiga), das 14h30m às 16h. O programa previsto é apresentado em seguida.
Emmanuel DrorFarjoun's magical theory of localization
Lecture 1: The existence of geometric localization and an algebraic analogue.
From this point of view, geometric localization involves making spaces
equivalent to a point and modules equivalent to zero in some sort of
universal way.
Lecture 2: This localization includes completion at a prime.
The standard definition of completion at a prime is in fact only an
approximation to the better homological definition involving ext.
Lecture 3: Zabrodsky' lemma and consequences of Haynes Miller' solution of the Sullivan conjecture.
Miller' solution to the Sullivan conjecture amounts to saying that
finite simply connected complexes are local with respect to the killing
of the classifying spaces of finite groups. This allows us to reverse
the process of taking connected coverings of simply connected finite
complexes, provided we are willing to complete the spaces and restrict
to those for which the second homotopy group is finite.
Lecture 4: Applications of localization and completion to Hspaces and loop spaces.
We shall show that the process of trying to make finite complexes into
Hspaces by taking connected covers is doomed to failure. And although
the iterated loop spaces of localized spheres have power maps which are
null homotopic, a certain large number of loops is necessary before any
power map, even on a connected cover, is null homotopic.
