---
tag: J8NMVNHGXT
kind: concept
name: Free factor complex
sources:
  - wikipedia: en:53404024@r1349175765
    locator: Free factor complex
    note: adopted
    mention: wikipedia://en/53404024
    sections: [Summary]
same_as:
  wikidata: Q30593823
  wikipedia: Free factor complex
inventory: [D1QZNMF5YR]
---

## Summary

In mathematics, the **free factor complex** (sometimes also called the **complex of free factors**) is a [[free group|020Z5SEN27]] counterpart of the notion of the curve complex of a finite type surface. The free factor complex was originally introduced in a 1998 paper of Allen Hatcher and Karen Vogtmann. Like the curve complex, the free factor complex is known to be Gromov-hyperbolic. The free factor complex plays a significant role in the study of large-scale geometry of $\operatorname{Out}(F_n)$.