Duke Mathematical Journal

Convex polytopes, Coxeter orbifolds and torus actions

Michael W. Davis and Tadeusz Januszkiewicz

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J., Volume 62, Number 2 (1991), 417-451.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077296365

Digital Object Identifier
doi:10.1215/S0012-7094-91-06217-4

Mathematical Reviews number (MathSciNet)
MR1104531

Zentralblatt MATH identifier
0733.52006

Subjects
Primary: 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]
Secondary: 14M25: Toric varieties, Newton polyhedra [See also 52B20] 57S10: Compact groups of homeomorphisms

Citation

Davis, Michael W.; Januszkiewicz, Tadeusz. Convex polytopes, Coxeter orbifolds and torus actions. Duke Math. J. 62 (1991), no. 2, 417--451. doi:10.1215/S0012-7094-91-06217-4. https://projecteuclid.org/euclid.dmj/1077296365


Export citation

References

  • [Andreev] E. M. Andreev, On convex polyhedra in Lobačevskiĭ space, Math. USSR-Sb. 10 (1970), 413–440, English translation.
  • [Bloch, et al.] A. M. Bloch, H. Flaschka, and T. Ratiu, A convexity theorem for isospectral manifolds of Jacobi matrices in a compact Lie algebra, preprint, 1989.
  • [Brønsted] A. Brøndsted, An introduction to convex polytopes, Graduate Texts in Mathematics, vol. 90, Springer-Verlag, New York, 1983.
  • [Danilov] V. I. Danilov, The geometry of toric varieties, Uspekhi Mat. Nauk 33 (1978), no. 2(200), 85–134, 247, Russian Math. Surveys 33 (1978), 97–154.
  • [Davis 1] M. Davis, Smooth $G$-manifolds as collections of fiber bundles, Pacific J. Math. 77 (1978), no. 2, 315–363.
  • [Davis 2] M. W. Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. (2) 117 (1983), no. 2, 293–324.
  • [Davis 3] M. W. Davis, Some aspherical manifolds, Duke Math. J. 55 (1987), no. 1, 105–139.
  • [Delzant] T. Delzant, Hamiltoniens périodiques et images convexes de l'application moment, Bull. Soc. Math. France 116 (1988), no. 3, 315–339.
  • [Fried] D. Fried, The cohomology of an isospectral flow, Proc. Amer. Math. Soc. 98 (1986), no. 2, 363–368.
  • [Gromov] M. Gromov, Hyperbolic groups, Essays in group theory ed. S. N. Gersten, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263.
  • [Khovanskii] A. G. Khovanskiĭ, Hyperplane sections of polyhedra, toric varieties and discrete groups in Lobachevskiĭ space, Funktsional. Anal. i Prilozhen. 20 (1986), no. 1, 50–61, 96.
  • [Oda] T. Oda, Convex bodies and algebraic geometry—toric varieties and applications. I, Algebraic Geometry Seminar (Singapore, 1987), World Sci. Publishing, Singapore, 1988, pp. 89–94.
  • [Orlik-Raymond] P. Orlik and F. Raymond, Actions of the torus on $4$-manifolds. I, Trans. Amer. Math. Soc. 152 (1970), 531–559.
  • [Reisner] G. Reisner, Cohen-Macaulay quotients of polynomial rings, Advances in Math. 21 (1976), no. 1, 30–49.
  • [Thurston] W. Thurston, The geometry and topology of $3$-manifolds, Princeton University, 1977, reproduced lecture notes.
  • [Tomei] C. Tomei, The topology of isospectral manifolds of tridiagonal matrices, Duke Math. J. 51 (1984), no. 4, 981–996.
  • [Stanley 1] R. Stanley, The upper bound conjecture and Cohen-Macaulay rings, Studies in Appl. Math. 54 (1975), no. 2, 135–142.
  • [Stanley 2] R. Stanley, The number of faces of a simplicial convex polytope, Adv. in Math. 35 (1980), no. 3, 236–238.
  • [Stanley 3] R. Stanley, Combinatorics and commutative algebra, Progress in Mathematics, vol. 41, Birkhäuser Boston Inc., Boston, MA, 1983.
  • [van der Kallen] W. van der Kallen, Homology stability for linear groups, Invent. Math. 60 (1980), no. 3, 269–295.