New proof of the cobordism invariance of the index

DOI10.1090/S0002-9939-01-06250-5zbMath0997.58009arXivmath/0011237OpenAlexW1823573036MaRDI QIDQ2781257

Maxim Braverman

Publication date: 19 March 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0011237

zbMATH Keywords

Dirac operatormodel operatorHermitian vector bundleselfadjoint hypo-elliptic pseudo-differential operator

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Index theory and related fixed-point theorems on manifolds (58J20) Pseudodifferential and Fourier integral operators on manifolds (58J40)

Related Items (11)

Cobordism invariance of the family index ⋮ Perturbations of Dirac operators ⋮ A \(K\)-theory proof of the cobordism invariance of the index ⋮ The index of Callias-type operators with Atiyah-Patodi-Singer boundary conditions ⋮ Callias-type operators in von Neumann algebras ⋮ Cusp geometry and the cobordism invariance of the index ⋮ The Calderón projection: New definition and applications ⋮ Orbifold index cobordism invariance ⋮ Bordism invariance of the coarse index ⋮ On Carvalho’s $K$-theoretic formulation of the cobordism invariance of the index ⋮ Cobordism invariance and the well-definedness of local index

Cites Work

• Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
• A note on the cobordism invariance of the index
• Supersymmetry and Morse theory
• Deficiency indices for symmetric Dirac operators on manifolds with conic singularities
• Semiclassical asymptotics on covering manifolds and Morse inequalities
• Novikov type inequalities for differential forms with non-isolated zeros
• On the cobordism invariance of the index of Dirac operators
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