 ##  [Genus](/index.php/genus) 

  ##  [Genus](https://mathlogic.quantumdictionary.io/genus-0) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/index.php/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

An integer invariant of a connected closed surface that counts the number of 'handles' (for orientable surfaces) or, equivalently, the maximum number of disjoint simple closed curves whose removal does not disconnect the surface; for a closed orientable surface the genus g satisfies Euler characteristic χ = 2 − 2g.