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Higher Complex Torsion and the Framing Principle
Kiyoshi Igusa, Brandeis University, Waltham, MA

Memoirs of the American Mathematical Society
2005; 94 pp; softcover
Volume: 177
ISBN-10: 0-8218-3773-7
ISBN-13: 978-0-8218-3773-3
List Price: US$66
Individual Members: US$39.60
Institutional Members: US$52.80
Order Code: MEMO/177/835
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We prove that higher Franz-Reidemeister (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 FR-torsion 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 Miller-Morita-Mumford classes.

Table of Contents

  • Complex torsion
  • Definition of higher FR-torsion
  • Properties of higher FR-torsion
  • The framing principle
  • Proof of the framing principle
  • Applications of the framing principle
  • The stability theorem
  • Bibliography
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