# Fredholm map

## Definition

A **Fredholm map** is a smooth map of Hilbert manifolds whose differential at every point is a bounded linear Fredholm operator. The index of the Fredholm map is defined as the index of any of these Fredholm operators.

**Fredholm map** is a smooth map of Hilbert manifolds whose differential at every point is a bounded linear Fredholm operator. The index of the Fredholm map is defined as the index of any of these Fredholm operators.