Many Triangulated 3-Spheres

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dc.creatorPfeifle, Julian
dc.creatorZiegler, Günter M.
dc.date2002-11-30
dc.date2003-11-25
dc.date.accessioned2026-07-07T04:53:26Z
dc.date.available2026-07-07T04:53:26Z
dc.descriptionWe construct 2^{Ω(n^{5/4})} combinatorial types of triangulated 3-spheres on n vertices. Since by a result of Goodman and Pollack (1986) there are no more than 2^{O(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.
dc.description9 pages, 4 figures; Incorporated referee's comments; to appear in Math. Annalen
dc.identifierhttps://arxiv.org/abs/math/0212004
dc.identifierhttp://arxiv.org/abs/math/0212004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65845
dc.subjectMetric Geometry
dc.subjectCombinatorics
dc.subjectGeometric Topology
dc.subject52B11; 52B70, 57Q15
dc.titleMany Triangulated 3-Spheres
dc.typetext

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