Many triangulated 3-spheres |
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Authors: | Julian?Pfeifle Email author" target="_blank">Günter M?ZieglerEmail author |
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Institution: | (1) Inst. Mathematics, MA 6-2, TU Berlin, D-10623 Berlin, Germany;(2) Present address: Institut de Matemàtica, Universitat de Barcelona, E-08007 Barcelona, Spain |
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Abstract: | We construct combinatorial types of triangulated 3-spheres on n vertices. Since by a result of Goodman and Pollack (1986) there are no more than 2O(n log n) combinatorial types of simplicial 4-polytopes, this proves that asymptotically there are far more combinatorial types of triangulated 3-spheres than of simplicial 4-polytopes on n vertices. This complements results of Kalai (1988), who had proved a similar statement about d-spheres and (d+1)-polytopes for fixed d 4.Mathematics Subject Classification (1991): 52B11, 52B70, 57Q15Supported by the Deutsche Forschungsgemeinschaft within the European graduate program Combinatorics, Geometry, and Computation (GRK 588/1) and an MSRI post-doctoral fellowship.Partially supported by Deutsche Forschungs-Gemeinschaft (DFG), via the DFG Research Center Mathematics in the Key Technologies (FZT86), the Research Group Algorithms, Structure, Randomness (Project ZI 475/3), and a Leibniz grant (ZI 475/4). |
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