##  [Spectral Flow](/spectral-flow) 

  ##  [Spectral Flow](https://puremath.quantumdictionary.io/spectral-flow-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An integer-valued invariant of a continuous one-parameter family of self-adjoint Fredholm operators that counts, with sign and multiplicity, the net number of eigenvalues that pass through zero as the parameter varies; it links spectral data to topological indices.