# A Function obstruction to the Existence of Complex Structures

## TL;DR

This paper introduces a new function that acts as an obstruction to the integrability of almost-complex structures, simplifying the process of determining the existence of complex structures on manifolds.

## Contribution

The paper constructs a novel scalar function that serves as an obstruction to complex structure existence, providing an easier alternative to tensor-based methods.

## Key findings

- The function is non-zero for non-integrable almost-complex structures.
- Non-vanishing of the function implies the structure is not integrable.
- The function simplifies the detection of complex structures.

## Abstract

We construct a function for almost-complex Riemannian manifolds. Non-vanishing of the function for the almost-complex structure implies the almost-complex structure is not integrable. Therefore the constructed function is an obstruction for the existence of complex structures from the almost-complex structure. It is a function, not a tensor, so it is easier to work with.