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This article is cited in 9 scientific papers (total in 9 papers)
Homotopy classification of elliptic operators on stratified manifolds
V. E. Nazaikinskiia, A. Yu. Savinb, B. Yu. Sterninc
a M. V. Lomonosov Moscow State University
b Independent University of Moscow
c Moscow Institute of Electronic Engineering
Abstract:
We give a homotopy classification of elliptic operators on
a stratified manifold. Namely, we establish an isomorphism between the
set of elliptic operators modulo stable homotopy and the $K$-homology
group of the manifold. By way of application, we obtain an explicit
formula for the obstruction of Atiyah–Bott type to the existence
of Fredholm problems in the case of stratified manifolds.
DOI:
https://doi.org/10.4213/im781
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English version:
Izvestiya: Mathematics, 2007, 71:6, 1167–1192
Bibliographic databases:
    
UDC:
515.168.5+517.986.32
MSC: Primary 46L80; Secondary 19K33, 58J40
Received: 06.02.2006
Citation:
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Homotopy classification of elliptic operators on stratified manifolds”, Izv. RAN. Ser. Mat., 71:6 (2007), 91–118; Izv. Math., 71:6 (2007), 1167–1192
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/izv781https://doi.org/10.4213/im781 http://mi.mathnet.ru/eng/izv/v71/i6/p91
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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Nazaikinskii V., Savin A., Sternin B., “Elliptic Theory on Manifolds with Corners: II. Homotopy Classification and K-Homology”, C(*)-Algebras and Elliptic Theory II, Trends in Mathematics, 2008, 207–226
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V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Atiyah–Bott index on stratified manifolds”, Journal of Mathematical Sciences, 170:2 (2010), 229–237
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V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “On the Poincaré isomorphism in $K$-theory on manifolds with edges”, Journal of Mathematical Sciences, 170:2 (2010), 238–250
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Savin A.Yu., Sternin B.Yu., “Surgery and index formulas on stratified manifolds”, Dokl. Math., 80:1 (2009), 521–524
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Savin A.Yu., Sternin B.Yu., “Index formulas for stratified manifolds”, Differ. Equ., 46:8 (2010), 1145–1156
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A. Yu. Savin, B. Yu. Sternin, E. Schrohe, “On the index formula for an isometric diffeomorphism”, Journal of Mathematical Sciences, 201:6 (2014), 818–829
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Debord C., Lescure J.-M., Rochon F., “Pseudodifferential Operators on Manifolds With Fibred Corners”, Ann. Inst. Fourier, 65:4 (2015), 1799–1880
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A. Yu. Savin, B. Yu. Sternin, “Homotopy classification of elliptic problems associated with discrete group actions on manifolds with boundary”, Ufa Math. J., 8:3 (2016), 122–129
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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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