The next meeting of the Reading Seminar in Algebraic Geometry will be held on May 30, 2014 at 15:30 in Room 503 of IMI.

A talk on:

Geometric bar construction - 1

will be delivered by Peter Dalakov, Institute of Mathematics and Informatics.

Everybody is invited.

Abstract.
If X is  a topological space, and G a topological group, there exists a classifying space of G-bundles, BG, which is unique up to homotopy. It comes equipped with a universal G-bundle EG->BG. The most famous construction of these is due to Milnor.

In this seminar we are going to consider the geometric bar construction, due to Milgram and Dold-Lashof. It has the property that, if G is an abelian topological countable CW-group, then BG and EG are again topological groups and EG->BG is a topological group homomorphism.

Later, we are going to consider, following Gajer,  the case when X is a smooth (complex) manifold, and G a (complex) Lie group. Then BG and EG acquire  smooth (complex) space structure.