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Uspekhi Mat. Nauk, 2009, Volume 64, Issue 2(386), Pages 73–202 (Mi umn9283)  

This article is cited in 10 scientific papers (total in 10 papers)

Index theory and non-commutative geometry on foliated manifolds

Yu. A. Kordyukov

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: This paper gives a survey of the index theory of tangentially elliptic and transversally elliptic operators on foliated manifolds as well as of related notions and results in non-commutative geometry.

DOI: https://doi.org/10.4213/rm9283

Full text: PDF file (1480 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2009, 64:2, 273–391

Bibliographic databases:

UDC: 515.16+517.98+514.7
MSC: Primary 58B34; Secondary 19K56, 46L87, 58J42
Received: 11.01.2009

Citation: Yu. A. Kordyukov, “Index theory and non-commutative geometry on foliated manifolds”, Uspekhi Mat. Nauk, 64:2(386) (2009), 73–202; Russian Math. Surveys, 64:2 (2009), 273–391

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.Yu., “On the index of nonlocal elliptic operators for compact Lie groups”, Cent. Eur. J. Math., 9:4 (2011), 833–850  crossref  mathscinet  zmath  isi  elib  scopus
    2. Sternin B.Yu., “On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem”, Cent. Eur. J. Math., 9:4 (2011), 814–832  crossref  mathscinet  zmath  isi  elib  scopus
    3. Brüning J., Kamber F.W., Richardson K., “Index theory for basic Dirac operators on Riemannian foliations”, Noncommutative geometry and global analysis, Contemp. Math., 546, Amer. Math. Soc., Providence, RI, 2011, 39–81  crossref  mathscinet  zmath  isi
    4. Monthubert B., Nistor V., “The $K$-groups and the index theory of certain comparison $C^*$-algebras”, Noncommutative geometry and global analysis, Contemp. Math., 546, Amer. Math. Soc., Providence, RI, 2011, 213–224  crossref  mathscinet  zmath  isi
    5. M. R. Sandoval, “The wave trace of the basic Laplacian of a Riemannian foliation near a non-zero period”, Ann. Glob. Anal. Geom., 44:2 (2013), 217–244  crossref  mathscinet  zmath  isi  elib  scopus
    6. Y. A. Kordyukov, V. A. Pavlenko, “On Lefschetz formulas for flows on foliated manifolds”, Ufa Math. J., 7:2 (2015), 71–101  mathnet  crossref  isi  elib
    7. Nistor V., “Analysis on singular spaces: Lie manifolds and operator algebras”, J. Geom. Phys., 105 (2016), 75–101  crossref  mathscinet  zmath  isi  scopus
    8. Wulff Ch., “Ring and module structures on K -theory of leaf spaces and their application to longitudinal index theory”, J. Topol., 9:4 (2016), 1074–1108  crossref  mathscinet  zmath  isi  scopus
    9. Yu. A. Kordyukov, “Laplacians on smooth distributions”, Sb. Math., 208:10 (2017), 1503–1522  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    10. Dang T.I., “Traces of G-Operators Concentrated on Submanifolds”, Differ. Equ., 54:4 (2018), 468–475  crossref  zmath  isi  scopus
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