topology of smooth 4-manifolds and the theory of topological modular forms

4-manifolds and topological modular forms

We consider topologically twisted compactification of 6d (1,0) theories on 4-manifolds with flavor symmetry backgrounds.The effective 2d theory has (0,1) supersymmetry and, possibly, a residual flavor symmetry.The equivariant topological genus of this 2d theory produces a new invariant of the 4-manifold equipped with a principle bundle, valued in the ring of equivariant weakly holomorphic(topological) modular forms.We describe basic properties of this map and present a few simple examples.