Surgery and harmonic spinors

DOI10.1016/j.aim.2008.09.013zbMath1159.53021arXivmath/0606224OpenAlexW2120477491MaRDI QIDQ960575

Mattias Dahl, Bernd Ammann, Emmanuel Humbert

Publication date: 22 December 2008

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606224

zbMATH Keywords

eigenvalueDirac operatorsurgery

Mathematics Subject Classification ID

Spin and Spin({}^c) geometry (53C27) Surgery and handlebodies (57R65) Bordism and cobordism theories and formal group laws in algebraic topology (55N22)

Related Items

A splitting theorem for the Seiberg-Witten invariant of a homology \(S^1\times S^3\), Existence of Dirac eigenvalues of higher multiplicity, Relations between threshold constants for Yamabe type bordism invariants, Dirac-harmonic maps from index theory, Harmonic spinors on a family of Einstein manifolds, Manifolds with small Dirac eigenvalues are nilmanifolds, The spinorial energy functional on surfaces, Continuity of Dirac spectra, Mass endomorphism, surgery and perturbations, Spectral asymmetry of the massless Dirac operator on a 3-torus, Harmonic spinors on the Davis hyperbolic 4-manifold, Highly connected manifolds of positive $p$-curvature, Almost harmonic spinors, Geometry in the large of the kernel of Lichnerowicz Laplacians and its applications, Gaps in the differential forms spectrum on cyclic coverings, Surgery and the Spinorial τ-Invariant, Invertible Dirac operators and handle attachments on manifolds with boundary

Cites Work

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• Gaps in the differential forms spectrum on cyclic coverings
• The classification of simply connected manifolds of positive scalar curvature
• The topology of 4-manifolds
• Spineurs, opérateurs de Dirac et variations de métriques. (Spinors, Dirac operators and variations of the metrics)
• Harmonic spinors on Riemann surfaces
• Stability of the \(p\)-curvature positivity under surgeries and manifolds with positive Einstein tensor
• Generic metrics and connections on spin- and \(\text{spin}^c\)-manifolds
• Harmonic spinors
• Simply connected manifolds of positive scalar curvature
• Der erste Eigenwert des Dirac‐Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung
• Elliptic Partial Differential Equations of Second Order
• Surgery and the spectrum of the Dirac operator
• Equivalent Norms for Sobolev Spaces