Surgery obstructions of fibre bundles

DOI10.1016/0022-4049(92)90003-XzbMath0755.57013MaRDI QIDQ1193456

Andrew Ranicki, Wolfgang Lück

Publication date: 27 September 1992

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

signaturefundamental groupfibre bundlealgebraic surgery transferchain homotopy actioncharacteristic class formula for the signatureMishchenko symmetric signaturesurgery transfertwisted signature formulaWall surgery obstruction groups

Mathematics Subject Classification ID

Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Surgery obstructions, Wall groups (57R67) Fiber bundles in algebraic topology (55R10) Transfer for fiber spaces and bundles in algebraic topology (55R12) Surgery obstructions ((K)-theoretic aspects) (19J25)

Related Items (9)

A spectral sequence in surgery theory and manifolds with filtrations ⋮ The signature of a fibre bundle is multiplicative mod 4 ⋮ Transfer maps for triples of manifolds ⋮ Algebraic independence of generalized MMM-classes ⋮ The nonmultiplicativity of the signature modulo 8 of a fibre bundle is an Arf-Kervaire invariant ⋮ Structure sets of triples of manifolds ⋮ Obstructions to fibering a manifold ⋮ Topological classification of multiaxial \(U(n)\)-actions (with an appendix by Jared Bass) ⋮ Rational Pontryagin classes of Euclidean fiber bundles

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Induced representations and projective modules
• Equivariant L-theory. I
• Round L-theory
• The transfer maps induced in the algebraic \(K_ 0\)- and \(K_ 1\)-groups by a fibration. II
• Transfer on algebraic K-theory and Whitehead torsion for PL fibrations
• Equivariant surgery theories and their periodicity properties
• Induction and structure theorems for orthogonal representations of finite groups
• Odd order group actions and Witt classification of inner products
• Multiplicativity of signature
• Additive L-theory
• Equivariant \(L\)-theory. II
• A certain type of irregular algebraic surfaces
• Wall's surgery obstruction groups for GxZ
• Frobenius reciprocity of Hermitian forms
• The representation of groups by automorphisms of forms
• Novikov's higher signature and families of elliptic operators
• On the Index of a Fibered Manifold
• The S 1 -Transfer in Surgery Theory
• THE REAL SEMICHARACTERISTIC OF A FIBERED MANIFOLD
• The transfer maps induced in the algebraic $K_0$- and $K_1$-groups by a fibration I.
• On the wall Finiteness Obstruction for the Total Space of Certain Fibrations
• The Algebraic Theory of Surgery I. Foundations
• The Obstruction to the Finiteness of the Total Space of a Flat Bundle
• A Certain Subgroup of the Fundamental Group
• Algebraic L -Theory, I: Foundations

This page was built for publication: Surgery obstructions of fibre bundles