Summary: * Corresponding author. Tel.: #34-942-201522; fax: #34-942-201402.
E-mail addresses: firstname.lastname@example.org (C.A. Athanasiadis), email@example.com (F. Santos).
Partially supported by the GoK ran Gustafsson Foundation, Stockholm, Sweden.
Partially supported by grant PB97-0358 of the Spanish DireccioH n General de Ensen anza Superior e InvestigacioH n
Topology 41 (2002) 423}433
On the topology of the Baues poset of polyhedral subdivisions
Christos A. Athanasiadis , Francisco Santos *
Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Departamento de Matema& ticas, Estadn&stica y Computacio& n, Universidad de Cantabria, E-39071 Santander, Spain
Received 10 March 2000; accepted 5 September 2000
Given an a$ne projection : PPQ of convex polytopes, let (P, ) be the re"nement poset of proper
polyhedral subdivisions of Q which are induced by , in the sense of Billera and Sturmfels. Let
(P, ) be
the spherical subposet of -coherent subdivisions. It is proved here 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 re"nement poset of