Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The boundary of a Busemann space

Author: Philip K. Hotchkiss
Journal: Proc. Amer. Math. Soc. 125 (1997), 1903-1912
MSC (1991): Primary 20F32
MathSciNet review: 1425125
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $X$ be a proper Busemann space. Then there is a well defined boundary, $\partial X$, for $X$. Moreover, if $X$ is (Gromov) hyperbolic (resp. non-positively curved), then this boundary is homeomorphic to the hyperbolic (resp. non-positively curved) boundary.

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

  • [Bo] B. H. Bowditch, Minkowskian Subspaces of Non-positively Curved Subspaces, preprint.
  • [Br] Martin R. Bridson, Geodesics and curvature in metric simplicial complexes, Group theory from a geometrical viewpoint (Trieste, 1990) World Sci. Publ., River Edge, NJ, 1991, pp. 373–463. MR 1170372
  • [F] Eric M. Freden, Negatively curved groups have the convergence property. I, Ann. Acad. Sci. Fenn. Ser. A I Math. 20 (1995), no. 2, 333–348. MR 1346817
  • [GH] É. Ghys and P. de la Harpe (eds.), Sur les groupes hyperboliques d’après Mikhael Gromov, Progress in Mathematics, vol. 83, Birkhäuser Boston, Inc., Boston, MA, 1990 (French). Papers from the Swiss Seminar on Hyperbolic Groups held in Bern, 1988. MR 1086648
  • [G1] M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263. MR 919829,
  • [G2] M. Gromov, 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
  • [M] James R. Munkres, Topology: a first course, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1975. MR 0464128
  • [NS] Walter D. Neumann and Michael Shapiro, Equivalent automatic structures and their boundaries, Internat. J. Algebra Comput. 2 (1992), no. 4, 443–469. MR 1189673,
  • [P] Frédéric Paulin, Constructions of hyperbolic groups via hyperbolizations of polyhedra, Group theory from a geometrical viewpoint (Trieste, 1990) World Sci. Publ., River Edge, NJ, 1991, pp. 313–372. MR 1170371
  • [Sw] E. Swenson, Negatively Curved Groups and Related Topics, PhD Thesis, Brigham Young University (1993).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20F32

Retrieve articles in all journals with MSC (1991): 20F32

Additional Information

Philip K. Hotchkiss
Affiliation: Department of Mathematics, The University of St. Thomas, St. Paul, Minnesota 55015

Keywords: Busemann space, geodesic, proper
Received by editor(s): November 19, 1995
Communicated by: James E. West
Article copyright: © Copyright 1997 American Mathematical Society