A vanishing theorem for tautological classes of aspherical manifolds

DOI10.2140/gt.2021.25.47zbMath1469.55008arXiv1705.06232OpenAlexW2614666082MaRDI QIDQ2024586

Markus Land, Fabian Hebestreit, Oscar Randal-Williams, Wolfgang Lück

Publication date: 4 May 2021

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.06232

zbMATH Keywords

characteristic classestautological classesaspherical closed manifoldsblock Borel conjectureBurghelea's conjecturemanifold bundles

Mathematics Subject Classification ID

Characteristic classes and numbers in differential topology (57R20) Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Poincaré duality spaces (57P10) Spectral sequences and homology of fiber spaces in algebraic topology (55R20) Microbundles and block bundles in algebraic topology (55R60)

Related Items (8)

Characteristic classes for families of bundles ⋮ Tautological classes of definite 4-manifolds ⋮ Simplicial volume and essentiality of manifolds fibered over spheres ⋮ ON THE COHOMOLOGY OF TORELLI GROUPS ⋮ Some rational homology computations for diffeomorphisms of odd‐dimensional manifolds ⋮ L‐theory of C∗$C^*$‐algebras ⋮ TAUTOLOGICAL RINGS AND STABILISATION ⋮ A homological approach to pseudoisotopy theory. I.

Cites Work

• Unnamed Item
• Unnamed Item
• The Farrell-Jones conjecture for arbitrary lattices in virtually connected Lie groups
• The Borel conjecture for hyperbolic and CAT(0)-groups
• Equivariant ordinary homology and cohomology
• Automorphisms of manifolds and algebraic K-theory. II
• Automorphism groups of polycyclic-by-finite groups and arithmetic groups.
• Coefficients for the Farrell-Jones conjecture
• The cyclic homology of the group rings
• Cyclic homology of groups and the Bass conjecture
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Groups of automorphisms of manifolds. With an appendix by E. Peders en
• Convergence groups and Seifert fibered 3-manifolds
• Fundamental groups of aspherical manifolds and maps of non-zero degree
• On the Farrell-Jones conjecture for Waldhausen's \(A\)-theory
• The homology of the mapping class group
• The lower algebraic \(K\)-theory of virtually infinite cyclic groups
• Nilpotency of Connes' periodicity operator and the idempotent conjectures
• On the tautological ring of \(\mathcal{M}_ g\)
• 4-manifold topology. I: Subexponential groups
• Stable moduli spaces of high-dimensional manifolds
• Rational homotopy theory of automorphisms of manifolds
• Riemannian hyperbolization
• Dimension of elementary amenable groups
• Homological stability for moduli spaces of high dimensional manifolds. II.
• Microbundles are fibre bundles
• An upper bound for the pseudoisotopy stable range
• Generalised Miller-Morita-Mumford classes for block bundles and topological bundles
• The stable moduli space of Riemann surfaces: Mumford's conjecture
• The \(K\)-theoretic Farrell-Jones conjecture for hyperbolic groups
• Microbundles and bundles. I: Elementary theory
• The microbundle representation theorem
• Algebraic K-theory III. Hermitian K-theory and geometric applications. Proceedings of the conference held at the Seattle Research Center of the Battelle Memorial Institute, from August 28 to September 8, 1972
• The Farrell–Jones conjecture forS-arithmetic groups
• Rigidity and characteristic classes of smooth bundles with nonpositively curved fibers
• A vanishing theorem for characteristic classes of odd-dimensional manifold bundles
• Tautological rings for high-dimensional manifolds
• Characteristic Classes and Homogeneous Spaces, I
• Rigidity and other topological aspects of compact nonpositively curved manifolds
• Poincare Duality and Fibrations
• Unitary nilpotent groups and Hermitian $K$-theory. I
• Pull-Backs in Homotopy Theory
• Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88)
• Fibrations with Compact Fibres
• Homological stability for moduli spaces of high dimensional manifolds. I
• Algebraic K-theory, assembly maps, controlled algebra, and trace methods
• Burghelea conjecture and asymptotic dimension of groups
• A fibre bundle description of Teichmüller theory
• The Farrell-Jones Conjecture for cocompact lattices in virtually connected Lie groups
• Closed aspherical manifolds with center
• On the Farrell-Jones Conjecture and its applications
• Divisibility of the stable Miller-Morita-Mumford classes
• A Certain Subgroup of the Fundamental Group
• Characteristic classes of surface bundles
• Convergence groups are Fuchsian groups
• The stable mapping class group and \(Q(\mathbb C P^ \infty_ +)\).

This page was built for publication: A vanishing theorem for tautological classes of aspherical manifolds