Interiors of compact contractible a-manifolds are hyperbolic (N ≥ 5)

Journal of Differential Geometry

Volumn 45, Issue 1, 1997, Pages 1-33

  Ancel, Fredric D ^a   Guilbault, Craig R ^b  

^a UNIVERSITY OF BONN   (Germany)

^b UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030635294     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214459752     Document Type: Article

References (20)

1. A. D. Aleksandrov, A theorem on triangles in a metric space and some applications, Trudy Mat. Inst. Steklov 38 (1951) 5-23.
2. A. D. Aleksandrov, Uber eine Verailgemeinerung der Riemannachen Geometric, Schritten Forschungsinst. Math. 1 (1957) 33-84.
3. A. D. Aleksandrov, V. N. Berestovskii &I. G. Nikolaev, Generalized Riemannian spaces, Russian Math. Surveys 41 (1986) 1-54.
4. F. D. Ancel &C. R. Guilbault, Compact contractible n-manifolds have arc spines (n >5), Pacffic J. Math. 168 (1995) 1-10.
5. W. Ballman, Singular spaces of non-positive curvature, Sur les grouses Hyperboliques d’aprbs Gromov, (E. Ghys and P. de la Harpe, eds.), Birkhauser, Basel, 1985, 189-201.
6. V. N. Berestovskii, Borsuk’s problem on the metrization of a polyhedron, Soviet Math. Dokl. 27 (1983) 56-59.
7. R. L. Bishop &B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969) 1-49.
8. J. W. Cannon, J. L. Bryant &R. C. Lacher, The structure of generalized manifolds having nonmanifold set of trivial dimension, Geometric Topology (J. C. Cantrell, ed.), Academic Press, New York, 1979, 261-300.
9. H. M. S. Coxeter, Non-Euclidean geometry, Univ. of Toronto Press, Toronto, Canada, 1942.
10. R. J. Daverman &F. C. Tinsley, Acyclic maps whose mapping cylinders embed in 5-manifolds, Houston J. Math. 16 (1990) 255-270.
11. M. W. Davis &T. Januszkiewicz, Hyperbolization of polyhedra, J. Differential Geom. 34 (1991) 347-388.
12. R. D. Edwards, The topology of manifolds and cell-like maps, Proc. Internat. Congress Math., Helsinki, 1978, (O.Lehti, ed.), Acad. Sci. Fenn., Helsinki, 1980, 111-127.
13. M. Gromov, Hyperbolic manifolds, groups and actions, Riemann Surfaces and Related Topics: Proc. 1978 Stony Brook Conference, (I. Kra and B. Maskit, eds.), Princeton University Press, Princeton, NJ, 1981, 183-215.
14. M. Gromov, Hyperbolic groups, Essays in group theory, (S. M. Gersten, ed.), Springer, Berlin, 1988, 75-264.
15. M. K. Kervaire, Smooth homology spheres and their fundamental groups, Trans. Amer. Math. Soc. 144 (1969) 67-72.
16. R. C. Kirby &L. C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969) 742-749.
17. F. Quinn, An obstruction to the resolution of homology manifolds, Michigan Math. J. 31 (1987) 286-292.
18. D. Rolfsen, Strongly convex metrics in cells, Bull. Amer. Math. Soc. 74 (1968) 171-175.
19. P. Thurston, The topology of 4-dimensional G-spaces and a study of 4-manifolds of non-positive curvature, Ph.D. thesis, Univ. of Tennessee, Knoxville, 1993.
20. M. Troyanov, Espaces à courbure négative et groupes hyperboligues, Sur les groupes Hyperboliques d’aprés Gromov, (E. Ghys and P. de la Harpe, eds.), Birkhâuser, Basel, 1985, 47-66