MappingClassGroup 2004-12-11 03:08:36 2004-12-11 16:30:20 Definition diffeotopy % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here Since the set of diffeomorphisms of a manifold which are \PMlinkname{diffeotopic}{Diffeotopy} to the identity is a normal subgroup of the group of all diffeomorphisms, we can form the quotient of the diffeomorphism group by this subgroup. This quotient is known as the \emph{ mapping class group}.