##  [Branch Point](/branch-point) 

  ##  [Branch Point](https://mathlogic.quantumdictionary.io/branch-point-0) 

  

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

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A point in the domain of a multivalued complex function where analytic continuation along closed loops around the point produces different values (nontrivial monodromy), so that a single-valued branch cannot be defined on any neighborhood that contains a loop encircling the point.

 

 

 

 

 





 

 



 ##  [Branch Point](https://puremath.quantumdictionary.io/branch-point-1) 

  

 [![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

A point a in the complex plane around which analytic continuation of a multi-valued function fails to return to its original value, forcing multiple sheets or branch cuts; monodromy around the point is nontrivial.

 

 

 

 

 





 

 



 ##  [Branch Point](https://algebra.quantumdictionary.io/branch-point-2) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A point in a covering map or projection where two or more local sheets meet and the local degree of the map drops; locally the map fails to be a homeomorphism (or is not locally bijective) because distinct preimages coalesce.