Contributions to the spectral geometry of locally homogeneous spaces
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Sebastian Boldt
Abstract
We report on several new results concerning the spectral geometry of locally homogeneous spaces. The first is a systematic method for constructing Dirac isospectral lens spaces, including many examples. The second is the result that many sixth-order curvature invariants - in particular, the integral of |∇R|2 - are not determined by the Laplace spectrum of a closed Riemannian manifold. The third establishes irreducibility of Laplace eigenspaces associated with generic left invariant metrics on certain compact Lie groups.
Abstract
We report on several new results concerning the spectral geometry of locally homogeneous spaces. The first is a systematic method for constructing Dirac isospectral lens spaces, including many examples. The second is the result that many sixth-order curvature invariants - in particular, the integral of |∇R|2 - are not determined by the Laplace spectrum of a closed Riemannian manifold. The third establishes irreducibility of Laplace eigenspaces associated with generic left invariant metrics on certain compact Lie groups.
Kapitel in diesem Buch
- Frontmatter I
- Contents V
- Introduction VII
- Algebraic K-theory, assembly maps, controlled algebra, and trace methods 1
- Lorentzian manifolds with special holonomy – Constructions and global properties 51
- Contributions to the spectral geometry of locally homogeneous spaces 69
- On conformally covariant differential operators and spectral theory of the holographic Laplacian 90
- Moduli and deformations 116
- Vector bundles in algebraic geometry and mathematical physics 150
- Dyson–Schwinger equations: Fix-point equations for quantum fields 186
- Hidden structure in the form factors of N = 4 SYM 197
- On regulating the AdS superstring 221
- Constraints on CFT observables from the bootstrap program 245
- Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities 266
- Yangian symmetry inmaximally supersymmetric Yang-Mills theory 288
- Wave and Dirac equations on manifolds 324
- Geometric analysis on singular spaces 349
- Singularities and long-time behavior in nonlinear evolution equations and general relativity 417
- Index 491
Kapitel in diesem Buch
- Frontmatter I
- Contents V
- Introduction VII
- Algebraic K-theory, assembly maps, controlled algebra, and trace methods 1
- Lorentzian manifolds with special holonomy – Constructions and global properties 51
- Contributions to the spectral geometry of locally homogeneous spaces 69
- On conformally covariant differential operators and spectral theory of the holographic Laplacian 90
- Moduli and deformations 116
- Vector bundles in algebraic geometry and mathematical physics 150
- Dyson–Schwinger equations: Fix-point equations for quantum fields 186
- Hidden structure in the form factors of N = 4 SYM 197
- On regulating the AdS superstring 221
- Constraints on CFT observables from the bootstrap program 245
- Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities 266
- Yangian symmetry inmaximally supersymmetric Yang-Mills theory 288
- Wave and Dirac equations on manifolds 324
- Geometric analysis on singular spaces 349
- Singularities and long-time behavior in nonlinear evolution equations and general relativity 417
- Index 491
