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On spaces of polynomial growth with no conjugate points
Author(s):
N.
D.
Lebedeva
Translated by:
the author
Original publication:
Algebra i Analiz,
tom 16
(2004),
vypusk 2.
Journal:
St. Petersburg Math. J.
16
(2005),
341-348.
MSC (2000):
Primary 57N16
Posted:
March 9, 2005
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Abstract:
The following generalization of the Hopf conjecture is proved: if the fundamental group of an  -dimensional compact polyhedral space  without boundary and with no conjugate points has polynomial growth, then there exists a finite covering of  by a flat torus.
References:
-
- [BB]
- W. Ballmann and M. Brin, Orbihedra of nonpositive curvature, Inst. Hautes Études Sci. Publ. Math. No. 82 (1995), 169-209 (1996). MR 1383216 (97i:53049)
- [BI]
- D. Burago and S. Ivanov, Riemannian tori without conjugate points are flat, Geom. Funct. Anal. 4 (1994), no. 3, 259-269. MR 1274115 (95h:53049)
- [C]
- C. Croke, Volumes of balls in manifolds without conjugate points, Internat. J. Math. 3 (1992), 455-467. MR 1168355 (93e:53048)
- [G1]
- M. Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. No. 53 (1981), 53-73. MR 0623534 (83b:53041)
- [G2]
- -, Asymptotic invariants of infinite groups, Geometric Group Theory. Vol. 2 (Sussex, 1991), London Math. Soc. Lecture Note Ser., vol. 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1-295. MR 1253544 (95m:20041)
- [I]
- S. V. Ivanov, The geometry of periodic metrics, and volumes of limit Finsler manifolds, Abstract of Thesis Prepared by Candidate, St. Petersburg, 1995.
- [TG]
- J. Tits, Appendix to: ``Groups of polynomial growth and expanding maps'' by M. Gromov, Inst. Hautes Études Sci. Publ. Math. No. 53 (1981), 74-78. MR 0623535 (83b:53042)
- [L1]
- N. D. Lebedeva, Exponential growth of spaces without conjugate points, Algebra i Analiz 15 (2003), no. 1, 184-200; English transl., St. Petersburg Math. J. 15 (2004), no. 1, 127-137. MR 1979721
- [L2]
- -, On the fundamental group of a compact space without conjugate points, PDMI Preprint no. 05/2002, S.-Peterburg. Otdel. Mat. Inst. (POMI), St. Petersburg, 2002.
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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:
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):
18/FEB/2003
Posted:
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).
Copyright of article:
Copyright
2005,
American Mathematical Society
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