Affine hom-complexes
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.
Cite
@article{arxiv.1407.6870,
title = {Affine hom-complexes},
author = {M. Bakuradze and A. Gamkrelidze and J. Gubeladze},
journal= {arXiv preprint arXiv:1407.6870},
year = {2016}
}
Comments
final version, to appear in Portugaliae Mathematica