Документ взят из кэша поисковой машины. Адрес
оригинального документа
: http://www.mccme.ru/dubna/2014/courses/dehornoy.htm
Дата изменения: Thu Jul 24 11:14:55 2014 Дата индексирования: Sun Apr 10 12:03:04 2016 Кодировка: koi8-r |
P. Dehornoy пїп»п°пЅпёяЂяѓпµя‚ пїяЂпѕпІпµяЃя‚пё 3 п·п°пЅяЏя‚пёяЏ.
Imagine an elastic disc floating freely in space. It can take many forms. Now project this disc on a horizontal plane. Which form do you see? Almost anything is possible. The projection of the boundary of this disc is the projection of a circle in the space, and can be any closed curve.
Now suppose that your floating disc is never vertical, and look at his projection on a horizontal plane. Can we obtain as many forms as before? No. For example the projection of the boundary cannot be a figure-eight.
Which curves in the plane can be obtained by projecting the boundary of such a never-vertical-disc? The answer of this question is a theorem of Samuel Blank. Explaining and proving it is the main goal of this course. It is also a pretext to introduce and play with (one of) the most fundamental object of modern geometry and topology: the б«fundamental groupб» of a space.
There are no particular prerequisites for this course, except to understand a bit of english! The program should be roughly: