Nonpositive curvature of blow-ups

Selecta Mathematica, New Series

Volumn 4, Issue 4, 1998, Pages 491-547

  Davis, M ^a   Januszkiewicz, T ^b   Scott, R ^c  

^a OHIO STATE UNIVERSITY   (United States)

^b Santa Clara University   (United States)

^c UNIVERSITY OF WROC AW   (Poland)

Author keywords

Aspherical; Blow up; Hyperplane arrangement; Zonotope

Indexed keywords

EID: 54649084102     PISSN: 10221824     EISSN: 14209020     Source Type: Journal    
DOI: 10.1007/s000290050039     Document Type: Article

References (37)

1. [A] M.F. Atiyah. Convexity and commuting Hamiltonians. Bull. London Math. Soc 14 (1982), 1-15.
2. [AR] I. R. Aitchison and J. H. Rubinstein. An introduction to polyhedral metrics of nonpositive curvature on 3-manifolds. Geometry of Low-Dimensional Manifolds, Volume II. Cambridge University Press, 1990, pp. 127-161.
3. [BLSWZ] B. Björner, M. Las Vergnas, B. Sturmfels, N. White and G. Ziegler. Oriented Matroids. Cambridge University Press, Cambridge, 1993.
4. [Bo] N. Bourbaki. Groupes et algèbres de Lie. Chapters 4-6. Masson, Paris, 1981.
5. [Br] E. Brieskorn. Die Fundamentalgruppe des Raumes der regulären Orbits einer endlichen Komplexen Spiegelungsgruppe. Invent. Math. 12 (1971), 57-61.
6. [Bro] K. Brown. Buildings. Springer-Verlag, New York, 1989.
7. [Ca] S. Cappell. On homotopy invariance of higher signatures. Invent. Math. 33 (1976), 171-179.
8. [CD1] R. Charney and M. Davis. The K(π, 1)-problem for hyperplane complements associated to infinite reflection groups. Journal of the American Math. Soc. 8 (1995), 597-627.
9. [CD2] R. Charney and M. Davis. Finite K(π, 1)s for Artin Groups. Prospects in Topology (F. Quinn, ed.). Princeton Univ. Press, Princeton;
10. Annals of Math. Studies 138 (1995), 110-124.
11. [CD3] R. Charney and M. Davis. Strict hyperbolization. Topology (2) 34 (1995), 329-350.
12. [D1] M. Davis. Groups generated by reflections and aspherical manifolds not covered by Euclidean space. Ann. Math. 117 (1983), 293-326.
13. [D2] M. Davis. Some aspherical manifolds. Duke Math. J. 55 (1987), 105-139.
14. [D3] M. Davis. Nonpositive curvature and reflection groups. To appear in Handbook of Geometric Topology.
15. [DJ1] M. Davis and T. Januszkiewicz. Convex polytopes, Coxeter orbifolds, and torus actions. Duke Math J. 62 (1991), 417-451.
16. [DJ2] M. Davis and T. Januszkiewicz. Hyperbolization of polyhedra. J. Differential Geometry 34 (1991), 347-388.
17. [DP1] C. De Concini and C. Procesi. Wonderful models of subspace arrangements. Selecta Math., New ser. 1 (1995), 459-494.
18. [DP2] C. De Concini and C. Procesi. Hyperplane arrangements and holonomy equations. Selecta Math., New ser. 1 (1995), 495-535.
19. [De] P. Deligne. Les immeubles des groupes de tresses généralisés. Invent. Math. 17 (1972), 273-302.
20. [FH] H. Flaschka and L. Haine. Torus orbits in G/P. Pacific J. Math. 149 (1991), 251-292.
21. [FM] W. Fulton and R. MacPherson. A compactification of configuration spaces. Ann. Math. 139 (1994), 183-225.
22. [FN] R. H. Fox and L. Neuwirth. The braid groups. Math. Scand. 10 (1962), 119-126.
23. [G] M. Gromov. Hyperbolic groups in Essays in Group Theory, (S. M. Gersten, ed.). M.S.R.I. Publ. 8. Springer-Verlag, New York, 1987.
24. [GM] I. M. Gelfand and R. MacPherson. Geometry of Grassmannians and a generalization of the dilogarithm. Adv. in Math. 44 (1982), 279-312.
25. [GS] V. Guillemin and S. Sternberg. Convexity properties of the moment mapping. Invent. Math. 67 (1982), 491-513.
26. [Jur] J. Jurkiewicz. Torus embeddings, polyhedra, k*-actions, and homology. Dissert. Math. 236 (1985), 52-57.
27. [Kai] M. M. Kapranov. The permutoassociahedron, Mac Lane's coherence theorem and asymptotic zones for the KZ equation. J. Pure and Applied Algebra 85 (1993), 119-142.
28. [Ka2] M. M. Kapranov. Chow quotients of Grassmannians. I. Adv. in Sov. Math. 16 (1993), 29-110.
29. [Kh] M. Khovanov. Real K(π, 1) arrangements from finite root systems. Math. Research Letters 3 (1996), 261-274.
30. [KY] Y. Kodama and J. Ye. Toda lattices with indefinite metric II: topology of the isospectral manifolds. Preprint.
31. [MM] N. E. Mnëv and P. Mani. Lecture by Mani.
32. [Od] T. Oda. Convex Bodies and Algebraic Geometry. An Introduction to the Theory of Toric Varieties. Ergeb. Math. Grenzgeb. 15. Springer-Verlag, Berlin, 1988.
33. [NR] G. Niblo and L. Reeves. The geometry of cube complexes and the complexity of their fundamental groups. Preprint (1994).
34. [Sag] M. Sageev. Ends of group pairs and non-positively curved cube complexes. Proc. London Math. Soc. 71 (1995), 585-617.
35. n. Invent. Math. 88 (1988), 603-618.
36. [St] J. Stasheff. Homotopy associativity of H-spaces. I, II. Trans. Amer. Math. Soc. 108 (1963), 275-292.
37. [T] C. Tomei. The topology of the isospectral manifolds of tridiagonal matrices. Duke Math. J. 51 (1984), 981-996.