The boundary of a Busemann space

Hotchkiss, Philip

doi:10.1090/S0002-9939-97-04166-X

The boundary of a Busemann space
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by Philip K. Hotchkiss

Proc. Amer. Math. Soc. 125 (1997), 1903-1912

DOI: https://doi.org/10.1090/S0002-9939-97-04166-X

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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

B. H. Bowditch, Minkowskian Subspaces of Non-positively Curved Subspaces, preprint.
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
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
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, DOI 10.1007/978-1-4684-9167-8
M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263. MR 919829, DOI 10.1007/978-1-4613-9586-7_{3}
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
James R. Munkres, Topology: a first course, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1975. MR 0464128
Walter D. Neumann and Michael Shapiro, Equivalent automatic structures and their boundaries, Internat. J. Algebra Comput. 2 (1992), no. 4, 443–469. MR 1189673, DOI 10.1142/S021819679200027X
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
E. Swenson, Negatively Curved Groups and Related Topics, PhD Thesis, Brigham Young University (1993).