The universality theorem for neighborly polytopes
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In this note, we prove that every open primary basic semialgebraic set is stably equivalent to the realization space of a neighborly simplicial polytope. This in particular provides the final step for Mnëv‘s proof of the universality theorem for simplicial polytopes.
Mathematics Subject Classification (2000)52B40 52C40 14P10
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- A. Björner, M. Las Vergnas, B. Sturmfels, N. White, and G. M. Ziegler: Oriented matroids, second ed., Encyclopedia of Mathematics and its Applications, vol. 46, Cambridge University Press, Cambridge, 1999.Google Scholar
- J. Richter-Gebert: Mnëv’s universality theorem revisited, Sém. Lothar. Combin. 34 (1995), Art. B34h, (electronic).Google Scholar
- J. Richter-Gebert: Realization Spaces of Polytopes, Lecture Notes in Mathematics, vol. 1643, Springer, Berlin, 1996.Google Scholar
- J. Richter-Gebert: The universality theorems for oriented matroids and poly-topes, Advances in discrete and computational geometry (South Hadley, MA, 1996), Contemp. Math., vol. 223, Amer. Math. Soc., Providence, RI, 1999, 269–292.Google Scholar
- P. W. Shor: Stretchability of pseudolines is NP-hard, Applied Geometry and Discrete Mathematics — The Victor Klee Festschrift (P. Gritzmann and B. Sturmfels, eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 4, Amer. Math. Soc., Providence RI, 1991, 531–554.Google Scholar
- B. Sturmfels: Simplicial polytopes without the isotopy property, preprints of the Institute for Mathematics and Applications (1988), 5.Google Scholar
- G. M. Ziegler: Lectures on Polytopes, Graduate Texts in Mathematics, vol. 152, Springer, New York, 1995, Revised edition, 1998; seventh updated printing 2007.Google Scholar