Differential Geometry Working Seminar | Alexander Teeter | Freedman’s Results and Donaldson’s Exclusions: Classification of 4-manifolds by intersection forms

Alexander Teeter, University of Waterloo

Freedman’s Results and Donaldson’s Exclusions: Classification of 4-manifolds by intersection forms

We look at Serre's algebraic classification of symmetric integral unimodular forms, and then Freedman's topological classification of topological 4-manifolds by their intersection forms. After, we take a turn to looking at Donaldson's exclusions, finding that smooth 4-manifolds are not as well behaved. Time permitting, we will see how Donaldson's exclusions naturally lead to the existence of exotic \(\mathbb{R}^4\)s.

MC 5417