Adiabatic Limits, Nonmultiplicativity of Signature, and Leray Spectral Sequence
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Publication:3974172
DOI10.2307/2939276zbMath0736.58039OpenAlexW4249831554MaRDI QIDQ3974172
Publication date: 25 June 1992
Full work available at URL: https://doi.org/10.2307/2939276
Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Heat equation (35K05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Spectral sequences and homology of fiber spaces in algebraic topology (55R20) Serre spectral sequences (55T10)
Related Items (52)
The flat Grothendieck-Riemann-Roch theorem without adiabatic techniques ⋮ Index Theory and the Hypoelliptic Laplacian ⋮ Adiabatic limits of \(\eta \)-invariants and the Meyer functions ⋮ The index of Dirac operators on incomplete edge spaces ⋮ Hitchin-Thorpe inequality for noncompact Einstein 4-manifolds ⋮ Isometric group actions and the cohomology of flat fiber bundles ⋮ Riemann-Roch formulas for the Atiyah-Patodi-Singer \(\bmod\, k\) spectral flow and application to \(\bmod\, k\) index theory ⋮ Asymptotics of the spectrum of the Laplace operator on Riemannian sol-manifolds in the adiabatic limit ⋮ Comparison of two equivariant \(\eta\)-forms ⋮ Eta-invariants for parameter-dependent operators associated with an action of a discrete group ⋮ An extended variational formula for the Bismut-Cheeger eta form and its applications ⋮ The index formula for families of Dirac type operators on pseudomanifolds ⋮ Riemannian flows and adiabatic limits ⋮ Some geometric results on \(K\)-theory with \(\mathbb{Z}/k\mathbb{Z}\)-coefficients ⋮ Petites valeurs propres et classe d'Euler des S1-fibrés ⋮ Local index theory and the Riemann–Roch–Grothendieck theorem for complex flat vector bundles ⋮ Asymptotics of the eta invariant ⋮ Eta invariants of Dirac operators on circle bundles over Riemann surfaces and virtual dimensions of finite energy Seiberg-Witten moduli spaces ⋮ Twistor spaces and the general adiabatic expansions ⋮ Hodge and signature theorems for a family of manifolds with fibre bundle boundary ⋮ Eta-invariants, torsion forms and flat vector bundles ⋮ Equivariant eta forms and equivariant differential \(K\)-theory ⋮ Quantum Hall effect and Quillen metric ⋮ APS boundary conditions, eta invariants and adiabatic limits ⋮ The adiabatic limit of Schrödinger operators on fibre bundles ⋮ Functoriality of equivariant eta forms ⋮ A condensed proof of the differential Grothendieck–Riemann–Roch theorem ⋮ Adiabatic limits of Seifert fibrations, Dedekind sums, and the diffeomorphism type of certain 7-manifolds ⋮ Higher eta-invariants ⋮ A Hodge-type theorem for manifolds with fibered cusp metrics ⋮ An index theorem in differential \(K\)-theory ⋮ Hodge cohomology of gravitational instantons ⋮ Diabatic limit, eta invariants and Cauchy–Riemann manifolds of dimension 3☆ ⋮ Intersection homology with general perversities ⋮ Vanishing of cohomology groups and large eigenvalues of the Laplacian on \(p\)-forms ⋮ Circle Bundles and the Kreck-Stolz Invariant ⋮ Jumps of the eta-invariant. (With an appendix by Shmuel Weinberger: Rationality of \(\rho\)-invariants) ⋮ An Application of the Index Theorem for Manifolds with Fibered Boundaries ⋮ Unnamed Item ⋮ Complete noncompact \(\mathrm{G}_2\)-manifolds from asymptotically conical Calabi-Yau 3-folds ⋮ Real embedding and equivariant eta forms ⋮ The \(S^1\)-equivariant signature for semi-free actions as an index formula ⋮ The computation of \(\eta\)-invariants on manifolds with free circle action ⋮ Analytic surgery and the eta invariant ⋮ Spectral sequences and adiabatic limits ⋮ Formes de torsion analytique et familles des submersions I ⋮ Submersions and equivariant Quillen metrics ⋮ Collapsing and the differential form Laplacian: the case of a smooth limit space. ⋮ Gravitational Chern–Simons and the adiabatic limit ⋮ Functoriality of real analytic torsion forms. ⋮ The mathematical work of V. K. Patodi ⋮ Circle bundles, adiabatic limits of \(\eta\)-invariants and Rokhlin congruences
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