Mathematics of the USSR-Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mathematics of the USSR-Sbornik, 1985, Volume 50, Issue 1, Pages 137–150
DOI: https://doi.org/10.1070/SM1985v050n01ABEH002737
(Mi sm2281)
 

This article is cited in 6 scientific papers (total in 6 papers)

Volume and fundamental group of a manifold of nonpositive curvature

S. V. Buyalo
References:
Abstract: The relationship between the volume $v(M)$ and the fundamental group $\pi_1(M)$ of a closed manifold $M$ of nonpositive curvature $K_\sigma$, $-1\leqslant K_\sigma\leqslant0$, is studied. The main result asserts that if $\pi_1(M)$ does not contain nontrivial normal abelian subgroups, then
$$ v(M)\geqslant\beta_ne^{-\alpha_nD(M)}, $$
where $D(M)$ is the diameter of $M$ and $\alpha_n$$\beta_n>0$ depend only on the dimension of $M$. From this it follows, in particular, that for given $n\geqslant2$ and $C>0$ there exist only finitely many pairwise nonhomeomorphic $n$-dimensional closed $M$ with $-1\leqslant K_\sigma\leqslant0$ and $D(M)\leqslant C$.
Figures: 1.
Bibliography: 9 titles.
Received: 12.03.1983
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1983, Volume 122(164), Number 2(10), Pages 142–156
Bibliographic databases:
UDC: 512.54
MSC: Primary 53C20; Secondary 57R19
Language: English
Original paper language: Russian
Citation: S. V. Buyalo, “Volume and fundamental group of a manifold of nonpositive curvature”, Mat. Sb. (N.S.), 122(164):2(10) (1983), 142–156; Math. USSR-Sb., 50:1 (1985), 137–150
Citation in format AMSBIB
\Bibitem{Buy83}
\by S.~V.~Buyalo
\paper Volume and fundamental group of a~manifold of nonpositive curvature
\jour Mat. Sb. (N.S.)
\yr 1983
\vol 122(164)
\issue 2(10)
\pages 142--156
\mathnet{http://mi.mathnet.ru/sm2281}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=717671}
\zmath{https://zbmath.org/?q=an:0556.53024}
\transl
\jour Math. USSR-Sb.
\yr 1985
\vol 50
\issue 1
\pages 137--150
\crossref{https://doi.org/10.1070/SM1985v050n01ABEH002737}
Linking options:
  • https://www.mathnet.ru/eng/sm2281
  • https://doi.org/10.1070/SM1985v050n01ABEH002737
  • https://www.mathnet.ru/eng/sm/v164/i2/p142
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:322
    Russian version PDF:101
    English version PDF:12
    References:54
    First page:2
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024