Memoirs of the American Mathematical Society 2010; 131 pp; softcover Volume: 205 ISBN10: 0821851942 ISBN13: 9780821851944 List Price: US$69 Individual Members: US$41.40 Institutional Members: US$55.20 Order Code: MEMO/205/963
 In this paper the author proves Generalized Homotopy Lemmas. These type of results play an important role in the classification theory of \(*\)homomorphisms up to asymptotic unitary equivalence. Table of Contents  Prelude
 The basic homotopy lemma for higher dimensional spaces
 Purely infinite simple \(C^*\)algebras
 Approximate homotopy
 Super homotopy
 Postlude
 Bibliography
