A Callias-Type Index Theorem with Degenerate Potentials

DOI10.1080/03605302.2014.942740zbMath1316.58019arXiv1210.3275OpenAlexW2024127785MaRDI QIDQ5246645

Chris Kottke

Publication date: 21 April 2015

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.3275

zbMATH Keywords

Dirac operatorindex theoremasymptotically conic manifoldscattering manifold

Mathematics Subject Classification ID

Index theory and related fixed-point theorems on manifolds (58J20) First-order elliptic systems (35J46)

Related Items (13)

Partial Compactification of Monopoles and Metric Asymptotics ⋮ Equivariant Callias index theory via coarse geometry ⋮ A Cheeger-Müller theorem for manifolds with wedge singularities ⋮ The Spectral Shift Function and the Witten Index ⋮ Dimension of monopoles on asymptotically conic 3-manifolds: Figure 1. ⋮ An \(L^2\)-index formula for monopoles with Dirac-type singularities ⋮ The index of Callias-type operators with Atiyah-Patodi-Singer boundary conditions ⋮ Deformation theory of periodic monopoles (with singularities) ⋮ Scales, blow-up and quasimode constructions ⋮ Callias-type operators in C∗-algebras and positive scalar curvature on noncompact manifolds ⋮ Callias-type operators in von Neumann algebras ⋮ The Atiyah-Patodi-Singer index on manifolds with non-compact boundary ⋮ Low energy limit for the resolvent of some fibered boundary operators

Cites Work

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• Axial anomalies and index theorems on open spaces
• Resolvent at low energy and Riesz transform for Schrödinger operators on asymptotically conic manifolds. I.
• Recovering asymptotics of metrics from fixed energy scattering data
• On the index of Callias-type operators
• Callias' index theorem, elliptic boundary conditions, and cutting and gluing
• Pseudodifferential operators on manifolds with fibred boundaries.
• A \(K\)-theoretic relative index theorem and Callias-type Dirac operators
• An index theorem of Callias type for pseudodifferential operators
• Dimension of monopoles on asymptotically conic 3-manifolds: Figure 1.

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