| On The Topology Of The Baues Poset Of Polyhedral Subdivisions (2007) | |||||||||||||||
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| . Given an affine projection : P ! Q of convex polytopes, let !(P; ) be the refinement poset of proper polyhedral subdivisions of Q which are induced by , in the sense of Billera and Sturmfels. Let ! coh (P; ) be the spherical subposet of -coherent subdivisions. It is proved that the inclusion of the latter poset into the former induces injections in homology and homotopy. In particular, the poset !(P; ) is homotopically nontrivial. As a corollary, the equivalence of the weak and strong forms of the generalized Baues problem of Billera, Kapranov and Sturmfels is established. As special cases, these results apply to the refinement poset of proper polyhedral subdivisions of a point configuration and to the extension poset of a realizable oriented matroid. 1. Introduction Let : P ! Q be an affine projection of convex polytopes. The Baues poset !(P; ) is a combinatorial model for the space of all continuous sections of which lie in the boundary of P . It arose in the theory o... | |||||||||||||||
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