For more information about this meeting, contact Anatole Katok, Svetlana Katok.

Title: | Group theoretic Dehn fillings and exotic groups. |

Seminar: | Department of Mathematics Colloquium |

Speaker: | Denis Osin, City College, CUNY |

Abstract: |

I shall explain how the theory of Dehn fillings of complete
finite volume hyperbolic 3-manifolds can be translated to an algebraic
language and generalized using relatively hyperbolic groups. The most
important achievement in this direction is an algebraic analogue of
Thurston's hyperbolic Dehn surgery theorem. This result can be used to
answer some long standing questions in group theory. Here we mention
just some of them.
1) Does there exist a finitely generated group other than Z/2Z where
all nontrivial elements are conjugate?
2) A group G is called a (generalized) product of subgroups A,B if
for any element g of G there are elements a,b of A and B,
respectively, such that g=ab. Suppose that A and B satisfy the
ascending (or descending) chain condition for subgroups. Does G
satisfy the same condition? |

### Room Reservation Information

Room Number: | MB114 |

Date: | 09 / 13 / 2007 |

Time: | 04:00pm - 05:00pm |