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This article is cited in 7 scientific papers (total in 7 papers)
On the index of elliptic operators on manifolds with edges
V. E. Nazaikinskiia, A. Yu. Savinb, B. Yu. Sterninb, B.-W. Schulzec
a A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences
b Independent University of Moscow
c University of Potsdam
Abstract:
Necessary and sufficient conditions for the representation of the index of elliptic operators on manifolds with edges in the form of the sum of homotopy invariants of symbols on the smooth stratum and on the edge are found. An index formula is obtained for elliptic operators on manifolds with edges under symmetry conditions with respect to the edge covariables.
DOI:
https://doi.org/10.4213/sm1419
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English version:
Sbornik: Mathematics, 2005, 196:9, 1271–1305
Bibliographic databases:
    
UDC:
517.168.5
MSC: Primary 58J05, 58J20, 58J32; Secondary 19Kxx, 19Lxx
Received: 06.10.2004
Citation:
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, B.-W. Schulze, “On the index of elliptic operators on manifolds with edges”, Mat. Sb., 196:9 (2005), 23–58; Sb. Math., 196:9 (2005), 1271–1305
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/msb1419https://doi.org/10.4213/sm1419 http://mi.mathnet.ru/eng/msb/v196/i9/p23
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This publication is cited in the following articles:
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V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Homotopy classification of elliptic operators on stratified manifolds”, Izv. Math., 71:6 (2007), 1167–1192
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V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Noncommutative geometry and classification of elliptic operators”, Journal of Mathematical Sciences, 164:4 (2010), 603–636
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A. Yu. Savin, B. Yu. Sternin, “Surgery and index formulas on stratified manifolds”, Dokl. Math., 80:1 (2009), 521–524
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Debord C., Lescure J.-M., Nistor V., “Groupoids and an index theorem for conical pseudo-manifolds”, J. Reine Angew. Math., 628 (2009), 1–35
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A. Yu. Savin, B. Yu. Sternin, “Index formulas for stratified manifolds”, Differ. Equ., 46:8 (2010), 1145–1156
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M. V. Korovina, “Differential equations on manifolds with edge singularities in spaces with asymptotics”, Differ. Equ., 46:5 (2010), 702–710
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Nistor V., “Analysis on singular spaces: Lie manifolds and operator algebras”, J. Geom. Phys., 105 (2016), 75–101
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