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Transactions of the American Mathematical Society

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A bounding question for almost flat manifolds


Author: Shashidhar Upadhyay
Journal: Trans. Amer. Math. Soc. 353 (2001), 963-972
MSC (1991): Primary 57R19, 57R20; Secondary 55N22
DOI: https://doi.org/10.1090/S0002-9947-00-02669-6
Published electronically: September 15, 2000
MathSciNet review: 1804410
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Abstract | References | Similar Articles | Additional Information

Abstract: We study bounding question for almost flat manifolds by looking at the equivalent description of them as infranilmanifolds $\Gamma\backslash L\rtimes G/G$. We show that infranilmanifolds $\Gamma\backslash L \rtimes G/G$ bound if $L$ is a 2-step nilpotent group and $G$ is finite cyclic and acts trivially on the center of the nilpotent Lie group $L$.


References [Enhancements On Off] (What's this?)

  • 1. P. E. Conner and E. E. Floyd, Differential periodic maps, Springer, Berlin, 1964. MR 31:750
  • 2. F. T. Farrell and S. Zdravkovska, Do almost flat manifolds bound?, Michigan Math. J. 30 (1983), 199-208. MR 85j:57059
  • 3. M. W. Gordon, The unoriented cobordism classes of compact flat Riemannian manifolds, J. Diff. Geometry, 15 (1980), 81-90. MR 82a:57029
  • 4. M. L. Gromov, Almost flat manifolds, J. Differential Geom. 13 (1978), 230-241. MR 80h:53041
  • 5. G. Hamrick and D. C. Royster, Flat Riemannian manifolds are boundaries, Invent. Math. 66 (1982), 405-413. MR 83h:53051
  • 6. C. Kosniowski and R. E. Stong, ${\mathbb Z}_{2}^k$-actions and characteristic numbers, Indiana Univ. Math. Journal, 28, (1979), 725 - 743. MR 81d:57027
  • 7. A. I. Mal'cev, On a class of homogeneous spaces, Izv. Akad. Nauk SSSR Ser. Mat. 13 (1949), 9-32; English transl., Amer. Math. Soc. Transl. (1) 9 (1962), 276-307. MR 10:507d; MR 12:589e
  • 8. M. S. Raghunathan, Discrete Subgroups of Lie Groups, Springer-Verlag, Berlin-Heidelberg-New York, 1972. MR 58:22394a
  • 9. R. E. Stong, Equivalent bordism and ${\mathbb Z}_{2}^k$ actions, Duke Math. J. 37 (1970), 779-785. MR 42:6847

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Additional Information

Shashidhar Upadhyay
Affiliation: Department of Mathematical Sciences, SUNY at Binghamton, Binghamton, New York 13902-6000
Address at time of publication: Bloomberg L. P., 499 Park Avenue, New York, New York 10022
Email: sdhar@math.binghamton.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02669-6
Keywords: Almost flat manifolds, infranilmanifolds, Stiefel-Whitney numbers
Received by editor(s): August 3, 1999
Published electronically: September 15, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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