Memoirs of the American Mathematical Society 2005; 94 pp; softcover Volume: 177 ISBN10: 0821837737 ISBN13: 9780821837733 List Price: US$66 Individual Members: US$39.60 Institutional Members: US$52.80 Order Code: MEMO/177/835
 We prove that higher FranzReidemeister (FR) torsion satisfies the transfer property and a formula known as the "Framing Principle" in full generality. We use these properties to compute the higher FRtorsion for all smooth bundles with oriented closed even dimensional manifold fibers. We also show that the higher complex torsion invariants of bundles with closed almost complex fibers are multiples of generalized MillerMoritaMumford classes. Table of Contents  Complex torsion
 Definition of higher FRtorsion
 Properties of higher FRtorsion
 The framing principle
 Proof of the framing principle
 Applications of the framing principle
 The stability theorem
 Bibliography
