×

The topology of configuration spaces, convex polytopes, and representations of lattices. (English. Russian original) Zbl 0807.52012

Proc. Steklov Inst. Math. 193, 37-41 (1993); translation from Tr. Mat. Inst. Steklova 193, 37-41 (1992).
The universality theorem of the third author states, very loosely, that any semialgebraic set can be the realization space of some convex polytope. In this note, the authors discuss, without proof, this and several closely related results, concerning realization spaces of Grassmannians, configurations, polytopes and cones, and lattices. In special cases (“good” dimensions), these spaces will be connected and contractible, but generally they will not be; tables are given which present what is known.
For the entire collection see [Zbl 0785.00035].

MSC:

52B40 Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)
14M15 Grassmannians, Schubert varieties, flag manifolds
14P10 Semialgebraic sets and related spaces
PDFBibTeX XMLCite