The U(1)-topological elliptic genus is surjective

TL;DR

This paper proves that the topological elliptic genus from SU-manifolds to topological Jacobi forms can be lifted to connective forms and that this lift is surjective in homotopy, advancing understanding of elliptic genera.

Contribution

It establishes the surjectivity of the lift of the topological elliptic genus to connective topological Jacobi forms, a novel result in the field.

Findings

The topological elliptic genus lifts to connective topological Jacobi forms.

This lift is surjective in homotopy.

The result connects cobordism rings of SU-manifolds with topological Jacobi forms.

Abstract

We show that the topological elliptic genus from the cobordism ring of SU-manifolds to topological Jacobi forms lifts to connective topological Jacobi forms, and that this lift is surjective in homotopy.