Volkmar Welker

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Complexes of (not) connected graphs, hypergraphs and their ho-mology appear in the construction of knot invariants given by V. Vassiliev V1, V2, V4]. In this paper we study the complexes of not i-connected k-hypergraphs on n vertices. We show that the complex of not 2-connected graphs has the homotopy type of a wedge of (n ? 2)! spheres of dimension 2n ? 5.(More)
We provide a \toolkit" of basic lemmas for the comparison of homotopy types of homotopy colimits of diagrams of spaces over small categories. We show how this toolkit can be used on quite diierent elds of applications. We demonstrate this with respect to 1. Bjj orner's \Generalized Homotopy Complementation Formula" 4], 2. the topology of toric varieties, 3.(More)
We recall that the calculation of homology with integer coefficients of a simplicial complex reduces to the calculation of the Smith Normal Form of the boundary matrices which in general are sparse. We provide a review of several algorithms for the calculation of Smith Normal Form of sparse matrices and compare their running times for actual boundary(More)
Let (an)n≥0 be a sequence of complex numbers such that its generating series satisfies ∑ n≥0 ant n = h(t) (1−t)d for some polynomial h(t). For any r ≥ 1 we study the transformation of the coefficient series of h(t) to that of h〈r〉(t) where ∑ n≥0 anrt n = h 〈r〉(t) (1−t)d . We give a precise description of this transformation and show that under some natural(More)
We investigate the Koszul property for quotients of aane semigroup rings by semigroup ideals. Using a combinatorial and topological interpretation for the Koszul property in this context, we recover known results asserting that certain of these rings are Koszul. In the process, we prove a stronger fact, suggesting a more general deenition of Koszul rings.(More)