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Izvestiya: Mathematics, 2007, Volume 71, Issue 6, Pages 1167–1192
DOI: https://doi.org/10.1070/IM2007v071n06ABEH002386 (Mi im781) 		 
This article is cited in 10 scientific papers (total in 10 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
English version PDF (445 kB) Citations (10)
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DOI: https://doi.org/10.1070/IM2007v071n06ABEH002386
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.
Received: 06.02.2006
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2007, Volume 71, Issue 6, Pages 91–118
DOI: https://doi.org/10.4213/im781
Bibliographic databases:
UDC: 515.168.5+517.986.32
MSC: Primary 46L80; Secondary 19K33, 58J40
Language: English
Original paper language: Russian
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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\paper Homotopy classification of~elliptic~operators on stratified manifolds
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\pages 91--118
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  • https://www.mathnet.ru/eng/im/v71/i6/p91
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:217
    English version PDF:24
    References:80
    First page:3
     
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