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

This article is cited in 9 scientific papers (total in 9 papers)

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

Full text: PDF file (478 kB)
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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
Received: 10.07.2001 and 30.12.2003

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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    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  crossref  mathscinet  zmath  isi  elib
    2. Savin A., “Elliptic operators on manifolds with singularities and $K$-homology”, $K$-Theory, 34:1 (2005), 71–98  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Krainer Th., “On the expansion of the resolvent for elliptic boundary contact problems”, Ann. Global Anal. Geom., 35:4 (2009), 345–361  crossref  mathscinet  zmath  isi  elib
    5. Savin A.Yu., Sternin B.Yu., “Index formulas for stratified manifolds”, Differential Equations, 46:8 (2010), 1145–1156  crossref  mathscinet  zmath  isi  elib
    6. Savin A.Yu., “On the Index of Elliptic Operators Associated with a Diffeomorphism of a Manifold”, Doklady Mathematics, 82:3 (2010), 884–886  crossref  mathscinet  zmath  isi  elib
    7. A. Yu. Savin, “On the Index of Nonlocal Elliptic Operators Corresponding to a Nonisometric Diffeomorphism”, Math. Notes, 90:5 (2011), 701–714  mathnet  crossref  crossref  mathscinet  isi
    8. Savin A., Sternin B., “Index of Elliptic Operators For Diffeomorphisms of Manifolds”, J. Noncommutative Geom., 8:3 (2014), 695–734  crossref  mathscinet  zmath  isi
    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  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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