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Portugaliae Mathematica

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Volume 73, Issue 3, 2016, pp. 183–205
DOI: 10.4171/PM/1984

Published online: 2016-09-12

Affine hom-complexes

Malkhaz Bakuradze[1], Alexander Gamkrelidze[2] and Joseph Gubeladze[3]

(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 [6], [12]. 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 [14], which generalizes Lovász’ well-known construction [15] 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