Projections of Polytopes on the Plane and the Generalized Baues Problem
نویسنده
چکیده
Given an affine projection π : P → Q of a d-polytope P onto a polygon Q, it is proved that the poset of proper polytopal subdivisions of Q which are induced by π has the homotopy type of a sphere of dimension d− 3 if π maps all vertices of P into the boundary of Q. This result, originally conjectured by Reiner, is an analogue of a result of Billera, Kapranov and Sturmfels on cellular strings on polytopes and explains the significance of the interior point of Q present in the counterexample to their generalized Baues conjecture, constructed by Rambau and Ziegler.
منابع مشابه
Projections of Polytopes on the Plane and Thegeneralized Baues
Given an aane projection : P ! Q of a d-polytope P onto a polygon Q, it is proved that the poset of proper polytopal subdivisions of Q which are induced by has the homotopy type of a sphere of dimension d ? 3 if maps all vertices of P into the boundary of Q. This result, originally conjectured by Reiner, is an analogue of a result of Billera, Kapranov and Sturmfels on cellular strings on polyto...
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