Many triangulated odd-dimensional spheres

Eran Nevo; Francisco Santos; Stedman Wilson

doi:10.1007/s00208-015-1232-x

Many triangulated odd-dimensional spheres

Eran Nevo^*
, Francisco Santos
, Stedman Wilson

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

It is known that the (Formula presented.) -sphere has at most (Formula presented.) combinatorially distinct triangulations with n vertices, for every (Formula presented.). Here we construct at least (Formula presented.) such triangulations, improving on the previous constructions which gave (Formula presented.) in the general case (Kalai) and (Formula presented.) for (Formula presented.) (Pfeifle–Ziegler). We also construct (Formula presented.) geodesic (a.k.a. star-convex) n-vertex triangulations of the (Formula presented.) -sphere. As a step for this (in the case (Formula presented.)) we construct n-vertex 4-polytopes containing (Formula presented.) facets that are not simplices, or with (Formula presented.) edges of degree three.

Original language	English
Pages (from-to)	737-762
Number of pages	26
Journal	Mathematische Annalen
Volume	364
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-015-1232-x
State	Published - 1 Apr 2016

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Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

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AB - It is known that the (Formula presented.) -sphere has at most (Formula presented.) combinatorially distinct triangulations with n vertices, for every (Formula presented.). Here we construct at least (Formula presented.) such triangulations, improving on the previous constructions which gave (Formula presented.) in the general case (Kalai) and (Formula presented.) for (Formula presented.) (Pfeifle–Ziegler). We also construct (Formula presented.) geodesic (a.k.a. star-convex) n-vertex triangulations of the (Formula presented.) -sphere. As a step for this (in the case (Formula presented.)) we construct n-vertex 4-polytopes containing (Formula presented.) facets that are not simplices, or with (Formula presented.) edges of degree three.

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Many triangulated odd-dimensional spheres

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