Уваров Ф.В. - Группы и Алгебры Ли - 2. Quotients of Lie groups by Lie subgroups

00:00:14 Brief description of the current lecture 00:04:55 Lemma 1: G/H is Hausdorff and second countable 00:05:28 Proof of the lemma 1 00:19:34 Definition 1: Atlas on G/H 00:24:15 Proposition 1: about construction smooth structures on G/H 00:26:00 Question: how proposition 1 helps in constructing smooth structures on G/h 00:42:37 Proof of the proposition 1 00:58:34 What did we learn? 00:59:09 Definition 2: a fiber bundle 01:11:42 Lemma 2: if f_x is smooth, then f_y is smooth 01:18:04 Fiber bundle satisfies Lemma 2 01:19:51 Proposition 2: the action is smooth 01:21:04 Proof of the proposition 2 01:24:24 Proposition 3: if H is a normal subgroup, then G/H is a Lie group 01:26:33 Proof of the proposition 3 Ссылка на плейлист: #мгу #мехмат #уваров #группыли #алгебрыли