| Alexander's Trick |
Article Index for Alexander's |
Website Links For Trick |
Information AboutAlexander's Trick |
|
: defines a homeomorphism of the ball. A similar result, which is likewise named ''Alexander's trick'', states two homeomorphisms on ''D''''n''+1 which agree on the boundary, are Isotopic . This follows from the fact that every homeomorphism which fixes the boundary is isotopic to the identity relative to the boundary. In fact, if ''f'' : ''D''''n''+1 → ''D''''n''+1 satisfies ''f''(''x'') = ''x'' for all ''x'' ∈ ''S''''n'', then an isotopy connecting ''f'' to the identity is given by |
|
|