la lettre de topologie, , quelques figures rudimentaires, et surtout pour ceux qui veulent en savoir plus, des adresses et autres links intéressants... selon le parcours proposé par Lacan, un détour qu'imposent les questions proposées par la clinique.
- attention : la plupart des
schémas ou images ne s'affichent pas actuellement ; en attendant
que ce problème technique soit réglé, je laisse néanmoins
la trame de ces pages "topologie" qui proposent déjà quelques
liens sur d'autres sites de topologie.
A Klein bottle can be made from a rectangular piece of the plane by identifying the top and bottom edges using the same orientation, but identifying the left and right edges with opposite orientation (as in the formation of a Möbius band). The first step forms a tube, but the second step can not be carried out without causing self-intersection: the tube must pass through itself in order to attach the ends correctly.

The Klein bottle can not be embedded in three-space, but it can be immersed there.
To view the surface rotating in three-space, select the picture.
To see how rotation in four-space can produce local self-intersections, select the second picture.
The Klein bottle can be thought of as two Möbius
bands identified along their boundaries. To see the Klein bottle separate
into these pieces and recombine, select the third picture.
un noeud borroméen (cf. bienvenue en toposie)
tore
cross-cap
Description and pictures
of the standard image of the Möbius band embedded in R^3.
Description and pictures
of a Möbius band embedded in R^3 with three twists instead of one.