Elliptic Theory on Singular Manifolds

ISBN: 9781584885207 出版年：2005 页码：372 Nazaikinskii, Vladimir E Savin, Anton Yu Schulze, Bert-Wolfgang Chapman and Hall/CRC

I Singular Manifolds and Differential Operators GEOMETRY OF SINGULARITIES Preliminaries Manifolds with conical singularities Manifolds with edges ELLIPTIC OPERATORS ON SINGULAR MANIFOLDS Operators on manifolds with conical singularities Operators on manifolds with edges Examples of elliptic edge operators II Analytical Tools PSEUDODIFFERENTIAL OPERATORS Preliminary remarks Classical theory Operators in sections of Hilbert bundles Operators on singular manifolds Ellipticity and finiteness theorems Index theorems on smooth closed manifolds LOCALIZATION (SURGERY) IN ELLIPTIC THEORY The index locality principle Localization in index theory on smooth manifolds Surgery for the index of elliptic operators on singular manifolds Relative index formulas on manifolds with isolated singularities III Topological Problems INDEX THEORY Statement of the problem Invariants of interior symbol and symmetries Invariants of the edge symbol Index theorems Index on manifolds with isolated singularities Supplement. Classification of elliptic symbols with symmetry and K-theory Supplement. Proof of Proposition 5.16 ELLIPTIC EDGE PROBLEMS Morphisms The obstruction to ellipticity A formula for the obstruction in topological terms Examples. Obstructions for geometric operators IV Applications and Related Topics FOURIER INTEGRAL OPERATORS ON SINGULAR MANIFOLDS Homogeneous canonical (contact) transformations Definition of Fourier integral operators Properties of Fourier integral operators The index of elliptic Fourier integral operators Application to quantized contact transformations Example RELATIVE ELLIPTIC THEORY Analytic aspects of relative elliptic theory Topological aspects of relative elliptic theory INDEX OF GEOMETRIC OPERATORS ON MANIFOLDS WITH CYLINDRICAL ENDS Operators on manifolds with cylindrical ends Index formulas HOMOTOPY CLASSIFICATION OF ELLIPTIC OPERATORS The homotopy classification problem Classification on smooth manifolds Atiyah-de Rham duality Abstract elliptic operators and analytic K-homology Classification on singular manifolds Some applications LEFSCHETZ FORMULAS Main result Proof of the theorem Contributions of conical points as sums of residues Supplement. The Lefschetz number Supplement. The Sternin-Shatalov method APPENDICES Spectral Flow Eta Invariants Index of Parameter-Dependent Elliptic Families Bibliographic Remarks Bibliography Index