On the Sullivan Conjecture and the Adams Conjecture
This talk follows on from my previous talk about the Sullivan Conjecture on the smooth classification of complete intersections, where we encountered the following question:
“Amongst the diffeomorphism types of all smooth manifolds, what is special about the diffeomorphism types of complete intersections?”
The aim of this talk is to present a new approach to the Sullivan Conjecture, which relates it to the Adams Conjecture, an important conjecture in stable homotopy theory solving the problem of when vectors bundles are fibre homotopy equivalent.
In this setting, it is possible to formulate an hypothesis, inspired by ideas of Frank Quinn, which addresses the question above for complete intersections and, more generally, for a large class of smooth complex projective varieties.
This is part of joint work with Csaba Nagy.
Dr Diarmuid Crowley , University of Melbourne