Affine hom-complexes

2014/07/25 by Bakuradze, M., Gamkrelidze, A., Gubeladze, J.
#51A10 (Primary) #52A25 #52B70 (Secondary) #55U10 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1407.6870

Abstract

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 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 Lovasz' well-known construction [15] for graphs.

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