27 citations · 67 across the 12 of their papers we have counts for
12 papers
Trends in Topological Combinatorics
Dmitry N. Kozlov
This thesis opens with an introductory discussion, where the reader is gently led to the world of topological combinatorics, and, where the results of this Habilitationsschrift are…
Cohomology of colorings of cycles
Dmitry N. Kozlov
We compute the cohomology groups of the spaces of colorings of cycles, i.e., of the prodsimplicial complexes Hom(C_m,K_n). We perform the computation first with Z_2, and then with…
Chromatic numbers, morphism complexes, and Stiefel-Whitney characteristic classes
Dmitry N. Kozlov
Combinatorics, in particular graph theory, has a rich history of being a domain of successful applications of tools from other areas of mathematics, including topological methods.…
Discrete Morse Theory for free chain complexes
Dmitry N. Kozlov
We extend the combinatorial Morse complex construction to the arbitrary free chain complexes, and give a short, self-contained, and elementary proof of the quasi-isomorphism betwee…
Simple homotopy types of Hom-complexes, neighborhood complexes, Lovász complexes, and atom crosscut complexes
Dmitry N. Kozlov
In this paper we provide concrete combinatorial formal deformation algorithms, namely sequences of elementary collapses and expansions, which relate various previously extensively…
Collapsing along monotone poset maps
Dmitry N. Kozlov
We introduce the notion of nonevasive reduction, and show that for any monotone poset map , the simplicial complex {\tt NE}-reduces to , for any $Q\supseteq{…