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Izv. RAN. Ser. Mat., 2007, Volume 71, Issue 6, Pages 91–118 (Mi izv781)  

This article is cited in 8 scientific papers (total in 8 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

Full text: PDF file (777 kB)
References: PDF file   HTML file

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

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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. 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  crossref  mathscinet  zmath  isi
    2. V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Atiyah–Bott index on stratified manifolds”, Journal of Mathematical Sciences, 170:2 (2010), 229–237  mathnet  crossref  mathscinet
    3. 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  mathnet  crossref  mathscinet
    4. Savin A.Yu., Sternin B.Yu., “Surgery and index formulas on stratified manifolds”, Dokl. Math., 80:1 (2009), 521–524  crossref  mathscinet  mathscinet  zmath  isi  elib  elib
    5. Savin A.Yu., Sternin B.Yu., “Index formulas for stratified manifolds”, Differ. Equ., 46:8 (2010), 1145–1156  crossref  mathscinet  mathscinet  zmath  isi  elib  elib
    6. A. Yu. Savin, B. Yu. Sternin, E. Schrone, “On the index formula for an isometric diffeomorphism”, Journal of Mathematical Sciences, 201:6 (2014), 818–829  mathnet  crossref
    7. Debord C., Lescure J.-M., Rochon F., “Pseudodifferential Operators on Manifolds With Fibred Corners”, Ann. Inst. Fourier, 65:4 (2015), 1799–1880  crossref  zmath  isi  elib
    8. A. Yu. Savin, B. Yu. Sternin, “Homotopy classification of elliptic problems associated with discrete group actions on manifolds with boundary”, Ufa Math. Journal, 8:3 (2016), 122–129  mathnet  crossref  mathscinet  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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