Elliptic Theory on Singular Manifolds
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A01=Anton Yu. Savin
A01=Bert-Wolfgang Schulze
A01=Boris Yu. Sternin
A01=Vladimir E. Nazaikinskii
advanced elliptic operator analysis
Atiyah-Bott-Lefschetz theorem
Author_Anton Yu. Savin
Author_Bert-Wolfgang Schulze
Author_Boris Yu. Sternin
Author_Vladimir E. Nazaikinskii
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Category=PBM
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Category=PHU
Coboundary Operators
Collar Spaces
conical
Conical Point
Conical Singularities
cotangent
Cotangent Bundle
Dirac Operator
Edge Symbol
Elliptic Operators
Elliptic Pseudodifferential Operator
Elliptic Theory
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Fourier Integral Operators
Fredholm Operators
Homotopy Classification
Homotopy Invariance
Index Formula
Index Theorem
index theory
interior
Interior Symbol
nonisolated singularities
operator
partial differential equations
points
principal
Principal Symbol
Pseudodifferential Operators
Self-adjoint Elliptic Operators
Singular Manifold
smooth
Smooth Compact Manifold
Smooth Manifold
Sobolev spaces
Spectral Flow
symbol
topological invariants
vector
Vector Bundle
Product details
- ISBN 9780367392291
- Weight: 453g
- Dimensions: 178 x 254mm
- Publication Date: 25 Sep 2019
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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The analysis and topology of elliptic operators on manifolds with singularities are much more complicated than in the smooth case and require completely new mathematical notions and theories. While there has recently been much progress in the field, many of these results have remained scattered in journals and preprints.
Starting from an elementary level and finishing with the most recent results, this book gives a systematic exposition of both analytical and topological aspects of elliptic theory on manifolds with singularities. The presentation includes a review of the main techniques of the theory of elliptic equations, offers a comparative analysis of various approaches to differential equations on manifolds with singularities, and devotes considerable attention to applications of the theory. These include Sobolev problems, theorems of Atiyah-Bott-Lefschetz type, and proofs of index formulas for elliptic operators and problems on manifolds with singularities, including the authors' new solution to the index problem for manifolds with nonisolated singularities.
A glossary, numerous illustrations, and many examples help readers master the subject. Clear exposition, up-to-date coverage, and accessibility-even at the advanced undergraduate level-lay the groundwork for continuing studies and further advances in the field.
Nazaikinskii, Vladimir E.; Savin, Anton Yu.; Schulze, Bert-Wolfgang; Sternin, Boris Yu.
