Modul: MAT075 Zurich Graduate Colloquium

## What is... the generalized Poincaré conjecture?

Dr. Peter Feller talk

**Date:** 13.11.18 **Time:** 17.15 - 18.30 **Room:**

The Poincare Conjecture asserts that, if a 3-manifold appears to be the 3-sphere from the point of view of simple algebraic invariants, then it is the 3-sphere. We explain the statement and its generalizations to arbitrary dimensions, known as the Generalized Poincare Conjecture, in detail. We then turn to the resolution of the Poincare Conjecture for large dimensions by Smale, which surprisingly turns out to be much simpler than the 3-dimensional case. We will explain the fundamental difference between high and low-dimension that forms the core of Smale's argument in completely elementary terms and provide a very rough sketch of the proof.