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 Mat. Sb., 2004, Volume 195, Number 9, Pages 85–126 (Mi msb847)

Defect of index in the theory of non-local problems and the $\eta$-invariant

A. Yu. Savin, B. Yu. Sternin

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: This paper is concerned with elliptic theory on manifolds the boundary of which is a cover. Non-local boundary value problems are considered and their indices are calculated. The Atiyah–Patodi–Singer problem is studied on such manifolds. For non-trivial covers the defect of the index is calculated. The Poincaré duality is constructed in $K$-theory on the corresponding singular manifolds.

DOI: https://doi.org/10.4213/sm847

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English version:
Sbornik: Mathematics, 2004, 195:9, 1321–1358

Bibliographic databases:

UDC: 517.168.5
MSC: Primary 58J05, 58J20, 58J28, 58J32; Secondary 16E20, 19Kxx, 19Lxx

Citation: A. Yu. Savin, B. Yu. Sternin, “Defect of index in the theory of non-local problems and the $\eta$-invariant”, Mat. Sb., 195:9 (2004), 85–126; Sb. Math., 195:9 (2004), 1321–1358

Citation in format AMSBIB
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\paper Defect of index in the theory of non-local problems and the $\eta$-invariant
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\jour Sb. Math.
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\issue 9
\pages 1321--1358
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• http://mi.mathnet.ru/eng/msb847
• https://doi.org/10.4213/sm847
• http://mi.mathnet.ru/eng/msb/v195/i9/p85

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Savin A., Sternin B., “Boundary value problems on manifolds with fibered boundary”, Math. Nachr., 278:11 (2005), 1297–1317
2. Savin A., “Elliptic operators on manifolds with singularities and $K$-homology”, $K$-Theory, 34:1 (2005), 71–98
3. V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, B.-W. Schulze, “On the index of elliptic operators on manifolds with edges”, Sb. Math., 196:9 (2005), 1271–1305
4. Krainer Th., “On the expansion of the resolvent for elliptic boundary contact problems”, Ann. Global Anal. Geom., 35:4 (2009), 345–361
5. Savin A.Yu., Sternin B.Yu., “Index formulas for stratified manifolds”, Differential Equations, 46:8 (2010), 1145–1156
6. Savin A.Yu., “On the Index of Elliptic Operators Associated with a Diffeomorphism of a Manifold”, Doklady Mathematics, 82:3 (2010), 884–886
7. A. Yu. Savin, “On the Index of Nonlocal Elliptic Operators Corresponding to a Nonisometric Diffeomorphism”, Math. Notes, 90:5 (2011), 701–714
8. Savin A., Sternin B., “Index of Elliptic Operators For Diffeomorphisms of Manifolds”, J. Noncommutative Geom., 8:3 (2014), 695–734
9. A. Yu. Savin, “O gomotopicheskoi klassifikatsii ellipticheskikh zadach so szhatiyami i $K$-gruppakh sootvetstvuyuschikh $C^*$-algebr”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 64, no. 1, Rossiiskii universitet druzhby narodov, M., 2018, 164–179
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