### Geometry and Dynamics Seminar

# Vladlen Timorin

### (Jacobs University)

## "Moore's theorem"

** Date: ** |
Wed, April 22, 2009 |

** Time: ** |
14:00 |

** Place: ** |
Research I Seminar Room |

**Abstract:** A theorem of R. Moore (1924) characterizes topological quotients of
the 2-sphere that are homeomorphic to the 2-sphere. Namely, if E is a
closed equivalence relation on the 2-sphere such that all equivalence
classes are connected, non-separating, and do not coincide with the
whole sphere, then the quotient of the sphere by E is homeomorphic to
the 2-sphere. We will discuss some ideas of the proof of this
theorem, and a more general topological theory, describing abstract
topological spaces homeomorphic to the sphere.