Projections of Polytopes on the Plane and Thegeneralized Baues
نویسنده
چکیده
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 polytopes and explains the signiicance 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 the Generalized Baues Problem
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...
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