# Secondary Invariants for String Bordism and tmf

## TL;DR

This paper introduces a secondary invariant for string manifolds based on spectral invariants of Dirac operators, linking global analysis with homotopy theory and topological modular forms.

## Contribution

It constructs a new secondary invariant for string bordism using spectral invariants and proves a secondary index theorem connecting analysis and homotopy theory.

## Key findings

- Construction of a secondary Witten genus invariant.
- Proof of a secondary index theorem.
- Calculation via topological modular forms.

## Abstract

Using spectral invariants of Dirac operators we construct a secondary version of the Witten genus, a bordism invariant of string manifolds in dimensions $4m-1$. We prove a secondary index theorem which relates this global-analytic construction with its homotopy-theoretic analog. The latter will be calculated through its factorization over topological modular forms.