The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on October 28, 2014 at 14:00 in Room 478 of IMI.

A talk on:

„Two equivalent descriptions of the Poincare sphere”

will be delivered by Ljubomir Andreev, IMI - BAS.

Everybody is invited.

Abstract.

The Poincare sphere is known as the first example of 3 dimensional compact manifold for which the first homology group is trivial but it is not homeomorphic to S³. There are many different ways to construct this manifold due to its various applications in topology. In the present talk will be discussed the equivalence between two descriptions of this manifold. On one hand it is the coset S³/l*, where l* is the preimage under the two fold covering SU(2)→SO(3) of the group l  of isometries with center (0,0,0) of the regular icosahedron, and on the other hand it is the Brieskorn manifold

M(2,3,5)={(z₁, z₂, z₃) ∈ C³ | z₁² + z₂³ + z₃⁵ = 0, |z₁|² + |z₂|² + |z₃|² = 1}.