The stable Adams conjecture

Abstract: The Adams conjecture, perhaps one of the most celebrated results
in the subject of stable homotopy theory, was resolved by Quillen and
Sullivan independently in the 1970s.  Essentially, the Adams conjecture
says that the q-th Adams operation on topological K-theory composed with
the J-homomorphism can be deformed continuously to the J-homomorphism
itself if localized away from q. The stable enhancement of the Adams
conjecture (which is only possible in the complex case) claims that this
deformation can be achieved within the space of infinite loop maps from BU
to the classifying space of spherical bundles. We recently found that the
only accepted proof of the stable Adams conjecture, which is due to
Friedlander (1980), has a mistake. In this talk, I will explain the
mistake, reformulate the statement of the stable Adams conjecture, sketch
our new proof of the stable Adams conjecture and discuss some of the
ramifications. This is a work joint with N. Kitchloo.