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Published online: 2016-09-12
Affine hom-complexesMalkhaz Bakuradze, Alexander Gamkrelidze and Joseph Gubeladze (1) Tbilisi State University, Georgia
(2) Tbilisi State University, Georgia
(3) San Francisco State University, USA
For two general polytopal complexes the set of face-wise affine maps between them is shown to be a polytopal complex in an algorithmic way. The resulting algorithm for computing the affine hom-complex is analyzed in detail. There is also a natural tensor product of polytopal complexes, which is the left adjoint functor for Hom. This extends the corresponding facts from single polytopes, systematic study of which was initiated in , . Explicit examples of computations of the resulting structures are included. In the special case of simplicial complexes, the affine hom-complex is a functorial subcomplex of Kozlov’s combinatorial hom-complex , which generalizes Lovász’ well-known construction  for graphs.
Keywords: Polytope, affine map, face poset, hom-polytope, tensor product, simplicial complex, polyhedral complex, hom-complex
Bakuradze Malkhaz, Gamkrelidze Alexander, Gubeladze Joseph: Affine hom-complexes. Port. Math. 73 (2016), 183-205. doi: 10.4171/PM/1984