On Kontsevich's characteristic classes for higher dimensional sphere bundles. I: The simplest class

DOI10.1007/s00209-008-0396-4zbMath1216.57014OpenAlexW2061045528MaRDI QIDQ1022334

Tadayuki Watanabe

Publication date: 22 June 2009

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-008-0396-4

zbMATH Keywords

homology spheresphere bundles over spheresgroup of self-diffeomorphismsHirzebruch signature defectKontsevich characteristic class

Mathematics Subject Classification ID

Characteristic classes and numbers in differential topology (57R20) Topology of vector bundles and fiber bundles (57R22) Homotopy groups of special spaces (55Q52)

Related Items

Families of diffeomorphisms and concordances detected by trivalent graphs ⋮ Diffeomorphisms of discs ⋮ Rational Pontryagin classes and functor calculus ⋮ On Kontsevich's characteristic classes for higher-dimensional sphere bundles II: Higher classes ⋮ Bott–Taubes–Vassiliev cohomology classes by cut-and-paste topology ⋮ Rational Pontryagin classes of Euclidean fiber bundles ⋮ Some finiteness results for groups of automorphisms of manifolds ⋮ A homological approach to pseudoisotopy theory. I.

Cites Work

• Determination of the cobordism ring
• A proof of the Smale conjecture, \(Diff(S^ 3)\simeq O(4)\)
• Quantum field theory and the Jones polynomial
• Integral invariants of 3-manifolds
• Differentiable and combinatorial structures on manifolds
• A compactification of configuration spaces
• Casson invariant, signature defect of framed manifolds and the secondary characteristic classes of surface bundles
• Characteristic forms and geometric invariants
• On the structure of Hopf algebras
• The index of elliptic operators. III
• La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie
• The non-finite homotopy type of some diffeomorphism groups
• Groups of homotopy spheres. I
• An invariant for certain smooth manifolds
• Homologie singulière des espaces fibrés. Applications
• Differentiable Structures on Spheres
• On the Structure of Manifolds
• Characteristic Classes. (AM-76)
• FINITE TYPE INVARIANTS OF INTEGRAL HOMOLOGY 3-SPHERES
• Axioms for higher torsion invariants of smooth bundles
• Relative Characteristic Classes
• Gromoll groups, ${\text{Diff}}\,S^n$ and bilinear constructions of exotic spheres
• Diffeomorphisms for Hilbert manifolds and handle decomposition
• Diffeomorphisms of the 2-Sphere
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item