… Since in this work we consider only affine polyhedral complexes we will suppress ‘affine’. …
of the polytopal complex structures on the affine hom-complexes HomPi,Pjfi, due to the huge …

… A subset A of V is an affine subspace if and only if it is closed under affine linear … the smallest
affine set contains A. Therefore, every affine subset of V that contains all vis also contains A. …

… where for any union of polytopes P ⊂ Rd and any affine subspace K ⊂ Rd, we denote the
intersection of P with K by ιK(P) = P ∩ K, and λ = (λ1,...,λn). The Hom-complexes central to this …

… In Section 6, we develop an affine-compact version of the linear kernel for the more general
category Conv of all convex compact sets and affine maps. It leads to the correct version (…

We show Péter Csorba's conjecture that the graph homomorphism complex Hom(C 5 ,K n+2
) is homeomorphic to a Stiefel manifold, the space of unit tangent vectors to the n-…

… Now we consider relationships between the Hom complexes and the box complexes. As …
types of the Hom complexes. Thus, we now compare homotopy types between Hom(Kr …

… Let me just mention that the algebras of functions on a smooth affine variety are smooth. For
… The composition products (8.1) are induced by the composition in the Hom-complexes. Let …

… The dimension dim P of P is defined as the dimension of its affine hull. A supporting hyperplane
of P is defined as a hyperplane H satisfying that H ∩ P = ∅ and P lies in one of the two …

… for computing with tensor products and Hom complexes of chain complexes of any type in …
can obtain an explicit parameterization of the affine space of homotopy classes of chain maps …

… for persistent homology, cohomology, hom complexes, filtered simplicial complexes, filtered
… , we can obtain an explicit parameterization of the affine space of homotopy classes of chain …