Konstruktionsmethoden und das kombinatorische Homöomorphieproblem für Triangulationen kompakter semilinearer Mannigfaltigkeiten

  • U. von Pachner
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. [1]
    J.W. Alexander, The combinatorial theory of complexes, Ann. of Math. 31, 292–320 (1930).MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    A. Āltshuler, J. Bokowski, L. Steinberg, The classification of simplicial 3-spheres with nine vertices into polytopes and non polytopes, Discrete Math. 31 (1980), 115–124.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    D. W. Barnette, A proof of the lower bound conjecture for convex polypes, Pacific J. Math. 46 (1973), 349–354.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    L. J. Billera, C.W. Lee, A proof of the sufficiency of McMullen’s conditions for f-vectors of simplicial convex polytopes, J. Comb. Theory Ser. A 31 (1981), 237–255.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    H. Bruggesser, P. Mani, Shellable decompositions of cells and spheres, Math. Scand, 29 (1972), 197–205.MathSciNetMATHGoogle Scholar
  6. [6]
    G. Danaraj, V. Klee, Which spheres are shellable? Ann. of Discrete Math. 2 (1978), 33–52.MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    V. I. Danilov, Birational Geometry Of Toric 3-Folds, Math. USSR Izvestiya, Vol. 21 (1983), No. 2.Google Scholar
  8. [8]
    R. D. Edwards, The double suspension of a certain homology 3-sphere is S5, A.M.S. Notices 22 (1975), A-334.Google Scholar
  9. [9]
    F. Ehlers, Eine Klasse komplexer Mannigfaltigkeiten und die Auflösung einiger isolierter Singularitäten, Math. Ann. 218 (1975), 127–156.MathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    G. Ewald, Über die stellare Äquivalenz konvexer Polytope, Resultate der Math. 1 (1978), 54–60.MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    G. Ewald, Torische Varietäten und konvexe Polytope, Bericht Nr. 40/1985, Ruhr-Universität Bochum.Google Scholar
  12. [12]
    G. Ewald, G. C. Shephard, Stellar subdivisions of boundary complexes of convex polytopes, Math. Ann. 210 (1974), 7–16.MathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    L.C. Glaser, Geometrical Combinatorial Topology, Bd. 1, New York 1970.Google Scholar
  14. [14]
    B. Grünbaum, Convex Polytopes, Interscience, New York 1967.MATHGoogle Scholar
  15. [15]
    J. F. P. Hudson, Piecewise Linear Topology, New York: Benjamin 1969.MATHGoogle Scholar
  16. [16]
    B. Kind, P. Kleinschmidt, Schälbare Cohen-Macaulay Komplexe und ihre Parametrisierung, Math. Z. 167, 173–179 (1979).MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    P. Kleinschmidt, Stellare Abänderungen und Schälbarkeit von Komplexen und Polytopen, J. of Geom. 11/2, 161–176 (1978).MathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    P. Kleinschmidt, U. Pachner, Shadow-boundaries and cuts of convex polytopes. Mathematika 27 (1980), 58–63.MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    A. Mandel, Topology of Oriented Matroids, Ph. D. Thesis. University of Waterloo, Ontario, Canada 1982.Google Scholar
  20. [20]
    P. Mani, D.W. Walkup, A 3-sphere Counterexample to the W -path Conjecture, Math. of Operation Research 5 (1980), 595–598.MathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    P. Mc Mullen, The maximum numbers of faces oc a convex polytope, Mathematika 17, 179–184 (1970).MathSciNetCrossRefGoogle Scholar
  22. [22]
    T. Oda, Torus embeddings and applications, Tata Inst. Fund. Res., Bombay, Springer-Verlag, Berlin and New York, 1978.Google Scholar
  23. [23]
    U. Pachner, Bistellare Äquivalenz kombinatorischer Mannigfaltigkeiten. Arch. Math. 30, 89–98 (1978).MathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    U. Pachner, Über die bistellare Äquivalenz simplizialer Sphären und Polytope. Math. Z. 176, 565–576 (1981).MathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    U. Pachner, Diagonalen in Simplizialkomplexen, Geome. Ded. 24 (1987), 1–28.MathSciNetMATHGoogle Scholar
  26. [26]
    G. Reisner, Cohen-Macaulay quotients of polynomial rings, Adv. in Math. 21 (1976), 30–49.MathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    R. P. Stanley, Cohen-Macaulay rings and constructible polytopes, Bull. Amer. Math. Soc. 81, 133–135 (1975).MathSciNetCrossRefMATHGoogle Scholar
  28. [28]
    R. P. Stanley, The upper bound conjecture and Cohen-Macaulay rings, Stud. Appl. Math. 54, 135–142 (1975).MathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    R. P. Stanley, The number of faces of a simplicial convex polytope Adv. in Math. 35, 236–238 (1980).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Mathematische Seminar 1987

Authors and Affiliations

  • U. von Pachner
    • 1
  1. 1.Udo PachnerFakultät und Institut für MathematikBochum 1Germany

Personalised recommendations