12/10/2006, 14:00 — 15:00 — Room P3.10, Mathematics Building Joe Neisendorfer, University of Rochester
Application of Dror-Farjoun localization in Algebraic Topology
In the 1950s, Serre introduced localization at primes into
algebraic topology as a way of isolating the study of primary
information about homotopy groups. In the 1960s, various authors
including Sullivan, Quillen, Kan, and Bousfield realized that the
localization of modules in commutative algebra has an analogue in
algebraic topology which amounts to replacing a space by a new
space in which the homology and homotopy groups have been
localized. Since this new procedure applied to spaces it enabled
the construction of interesting spaces which exhibited desirable
phenomena in homotopy or homology. In the 1980s, Dror-Farjoun and
Bousfield studied a generalization of this which also included a
procedure to complete homotopy groups, construction which had
previously seemed very different from localization. This talk will
describe localization and completion in its various forms and some
surprising consequences that they have when combined with Miller's
solution to the Sullivan conjecture.
