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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

On spaces of polynomial growth with no conjugate points


Author: N. D. Lebedeva
Translated by: the author
Original publication: Algebra i Analiz, tom 16 (2004), nomer 2.
Journal: St. Petersburg Math. J. 16 (2005), 341-348
MSC (2000): Primary 57N16
Published electronically: March 9, 2005
MathSciNet review: 2068342
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Abstract | References | Similar Articles | Additional Information

Abstract: The following generalization of the Hopf conjecture is proved: if the fundamental group of an $n$-dimensional compact polyhedral space $M$ without boundary and with no conjugate points has polynomial growth, then there exists a finite covering of $M$ by a flat torus.


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Additional Information

N. D. Lebedeva
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191011, Russia
Email: lebed@pdmi.ras.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-05-00853-8
PII: S 1061-0022(05)00853-8
Keywords: $n$-dimensional polyhedral space, polyhedral pseudomanifold, fundamental group
Received by editor(s): February 18, 2003
Published electronically: March 9, 2005
Additional Notes: Partially supported by RFBR (grant no. 02-01-00090), by CRDF (grant no. RM1-2381-ST-02), and by SS (grant no. 1914.2003.1).
Article copyright: © Copyright 2005 American Mathematical Society