Séminaire des doctorants

# Seminar

## by Mr Dimitri Le Meur (Toulouse)

Europe/Paris
318 (IMB)

### 318

#### IMB

Description
"Mister... WHAT is a manifold ?! (Part I ?)"

Every PhD student know a little about manifolds. Nevertheless, its
formal definition hides difficulties. For instance, it is not explained
how the open sets join together (i.e the topological nature of their
multiple intersections, and how the open sets and their intersections
are linked together) ; this prevents to build explicitly manifold, and
prevents the comprehension and their classification.
We will talk here about the classification of topological manifolds. In
dimension 1, we show that the 2 connex manifolds possible are the circle
and the line. In dimension 2, all surfaces are triangulable ; this
enables to classify compact surfaces (actually, it enables to classify
all the surfaces, but we will not show this). For the dimensions greater
than 4, it is possible to use the complexity of the fundamental groups
to show that it impossible to classify manifolds (so it is impossible
answer the question of the title ! ).
We might talk in some other seminar of the Ricci flow, which enable to
classify manifolds in dimension 3 ; but it is a bit more complicated, so
it will be impossible to talk in detail of this topic (indeed, with 3
remunerated hardworking years it will be not certain we manage to make
it).
Organized by

Nicolas Massin

Organisateur
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