16/03/2005, 11:00 — 12:00 — Room P3.10, Mathematics Building Christopher J. Mulvey, University of Sussex / University of Cambridge
Sheaves of C*-algebras
In this informal talk, motivated by recent work in progress on sheaves in the context of noncommutative spaces, I shall examine some of the less known aspects of sheaves. On the one hand, I want to consider the way in which the fibre space and the functorial ways of defining sheaves adapt to allow one to consider sheaves, not just of sets, or groups, or rings, but of Banach spaces and C*-algebras. On the other hand, but closely linked with this approach, I want to recall the alternative way of considering sheaves as local sets, as it was developed by Higgs, and then by Fourman and Scott, from the Boolean-valued sets introduced by Scott as an alternative approach to proving the independence of the Continuum Hypothesis. All of which begins to indicate the way in which this may be extended to the noncommutative context of quantal sets over an involutive quantale, at least in the case of the quantales obtained by taking the spectrum of a C*-algebra, and of the quantales introduced by Resende in characterising localic étale groupoids.
