Faculty of Mathematics, Physics
and Informatics
Comenius University in Bratislava

Seminar of Differential and Algebraic Topology (Diarmuid Crowley)

Tuesday 3.9.2019 at 14:00, Lecture room M/116

21. 08. 2019 23.14 hod.
By: Tibor Macko

Diarmuid Crowley (Melbourne):
The smooth classification of complete intersections

A complete intersection X of complex dimension n is a smooth projective algebraic variety defined by the intersection of r hyper-surfaces in CP^{n+r}. A theorem of Serre states that the diffeomorphism type of X is determined by the r-tuple integers giving the degree of the hyper-surfaces. The total degree of X is the product of these degrees.

A conjecture of Sullivan, verified in many cases by Libgober and Wood and also Kreck states that complete intersections are classified up to diffeomorphism by their Pontrjagin numbers and their total degrees.

In this talk I report on work verifying Sullivan’s conjecture for n = 4. As time permits I will discuss how the Adams Conjecture from stable homotopy appears in the proof and how it might be involved in verifying Sullivan’s conjecture for all n.

This is joint work with Csaba Nagy.