RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Ufimsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Ufimsk. Mat. Zh., 2015, Volume 7, Issue 2, Pages 73–108 (Mi ufa280)  

On Lefschetz formulas for flows on foliated manifolds

Y. A. Kordyukova, V. A. Pavlenkob

a Institute of Mathematics, Russian Academy of Sciences, Chernyshevsky str., 112, 450008, Ufa, Russia
b Bashkir State Agrarian University, 50-letiya Oktyabrya Str., 34, 450001, Ufa, Russia

Abstract: The paper is devoted to the Lefschetz formulas for flows on compact manifolds, preserving a codimension one foliation and having fixed points. We develop an approach to the Lefschetz formulae based on the notion of the regularized trace on some algebra of singular integral operators introduced in a previous paper. The Lefschetz formula is proved in the case when the flow preserves a foliation given by the fibers of a fiber bundle over a circle. For a particular example of a flow on a two-dimensional torus, preserving a Reeb type foliation, we prove an analogue of the McKean–Singer formula for smoothed regularized Lefschetz functions.

Keywords: Lefschetz formula, flow, closed orbits, fixed points, foliated manifold, regularized trace.

Full text: PDF file (732 kB)
References: PDF file   HTML file

English version:
Ufa Mathematical Journal, 2015, 7:2, 71–101 (PDF, 508 kB); https://doi.org/10.13108/2015-7-2-71

Bibliographic databases:

Document Type: Article
MSC: 58J22, 37C25, 58J42
Received: 17.03.2015

Citation: Y. A. Kordyukov, V. A. Pavlenko, “On Lefschetz formulas for flows on foliated manifolds”, Ufimsk. Mat. Zh., 7:2 (2015), 73–108; Ufa Math. J., 7:2 (2015), 71–101

Citation in format AMSBIB
\Bibitem{KorPav15}
\by Y.~A.~Kordyukov, V.~A.~Pavlenko
\paper On Lefschetz formulas for flows on foliated manifolds
\jour Ufimsk. Mat. Zh.
\yr 2015
\vol 7
\issue 2
\pages 73--108
\mathnet{http://mi.mathnet.ru/ufa280}
\elib{http://elibrary.ru/item.asp?id=24188346}
\transl
\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 2
\pages 71--101
\crossref{https://doi.org/10.13108/2015-7-2-71}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000416602300006}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84937855345}


Linking options:
  • http://mi.mathnet.ru/eng/ufa280
  • http://mi.mathnet.ru/eng/ufa/v7/i2/p73

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • ”фимский математический журнал
    Number of views:
    This page:117
    Full text:37
    References:13

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019