Axioms for higher torsion invariants of smooth bundles

DOI10.1112/jtopol/jtm011zbMath1196.57024arXivmath/0503250OpenAlexW2075778225MaRDI QIDQ5451811

Kiyoshi Igusa

Publication date: 27 March 2008

Published in: Journal of Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503250

zbMATH Keywords

Reidemeister torsionhigher torsionMiller-Morita-Mumford classes

Mathematics Subject Classification ID

Characteristic classes and numbers in differential topology (57R20) Determinants and determinant bundles, analytic torsion (58J52) Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Whitehead (and related) torsion (19J10) Differential topological aspects of diffeomorphisms (57R50)

Related Items (14)

Axioms for higher twisted torsion invariants of smooth bundles ⋮ Scattering matrix and analytic torsion ⋮ An equivariant version of Hatcher'sG/Oconstruction: Figure 1. ⋮ Equivalence of higher torsion invariants ⋮ Exotic smooth structures on topological fiber bundles I ⋮ Exotic smooth structures on topological fiber bundles II ⋮ Gluing formula of real analytic torsion forms and adiabatic limit ⋮ The product theorem for parametrized homotopy Reidemeister torsion ⋮ Homotopy groups of the moduli space of metrics of positive scalar curvature ⋮ Twisted higher smooth torsion ⋮ Smooth parametrized torsion: A manifold approach ⋮ On Kontsevich's characteristic classes for higher dimensional sphere bundles. I: The simplest class ⋮ On Kontsevich's characteristic classes for higher-dimensional sphere bundles II: Higher classes ⋮ Differential function spectra, the differential Becker-Gottlieb transfer, and applications to differential algebraic 𝐾-theory

Cites Work

• Unnamed Item
• The stability theorem for smooth pseudoisotopies
• Axioms for bundle transfers and traces
• The transfer map and fiber bundles
• The signature of quasi-nilpotent fiber bundles
• The Borel regulator map on pictures. II: An example from Morse theory
• The product theorem for parametrized homotopy Reidemeister torsion
• A parametrized index theorem for the algebraic \(K\)-theory Euler class.
• Sur les difféomorphismes de la sphère de dimension trois \(\Gamma_ 4 = 0\)
• La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie
• Formes de torsion analytique et familles de submersions
• Rational Homotopy of the Space of Sections of a Nilpotent Bundle
• Flat Vector Bundles, Direct Images and Higher Real Analytic Torsion
• Higher complex torsion and the framing principle

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