Let be a topological Hausdorff space. Let be the group of homeomorphisms , which can be also turn into a topological space by means of the compact-open topology. And let be the k-th homotopy group functor.
Then the k-th homeotopy is defined as:
that is, the group of homotopy classes of maps . Which is different from , the group of homotopy classes of maps .
One important result for any low dimensional topologist is that for a surface
which is the ’s extended mapping class group.
G.S. McCarty, Homeotopy groups, Trans. A.M.S. 106(1963)293-304.
|Date of creation||2013-03-22 15:41:54|
|Last modified on||2013-03-22 15:41:54|
|Last modified by||juanman (12619)|
|Synonym||mapping class group|