31/10/2002, 14:00 — 15:00 — Sala P3.10, Pavilhão de Matemática Freddy Van Oystaeyen, University of Antwerp
Noncommutative topology and geometry
Trying to discover a unifying theory connecting the noncommutative
geometry of schematic algebras to the classical basis for quantum
mechanics and the noncommutative geometry in terms of C*-algebras,
we develop noncommutative topology both in the analytic sense or in
the sense of Grothendieck topology. The relation with the lattice
of linear closed subspaces of a Hilbert space H is indicated.
Function theory in a quaternion variable viewed as two noncommuting
complex variables is developed and leads to noncommutative Riemann
manifolds and other examples of noncommutative manifolds.
