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1,266
Combinatorial topology of toric arrangements
"... Abstract. We prove that the complement of a complexified toric arrangement has the homotopy type of a minimal CWcomplex, and thus its homology is torsionfree. To this end, we consider the toric Salvetti complex, a combinatorial model for the arrangement’s complement. Using diagrams of acyclic cate ..."
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Abstract. We prove that the complement of a complexified toric arrangement has the homotopy type of a minimal CWcomplex, and thus its homology is torsionfree. To this end, we consider the toric Salvetti complex, a combinatorial model for the arrangement’s complement. Using diagrams of acyclic
Some new directions in infinitecombinatorial topology
, 2004
"... We give a light introduction to selection principles in topology, a young subfield of infinitecombinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are stated. Some results which do not appear elsewhere are al ..."
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Cited by 19 (14 self)
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We give a light introduction to selection principles in topology, a young subfield of infinitecombinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are stated. Some results which do not appear elsewhere
Combinatorial Topology Of Multipartite Entangled States
, 2008
"... With any state of a multipartite quantum system its separability polytope is associated. This is an algebrotopological object (nontrivial only for mixed states) which captures the localisation of entanglement of the state. Particular examples of separabilty polytopes for 3partite systems are expli ..."
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Cited by 1 (1 self)
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With any state of a multipartite quantum system its separability polytope is associated. This is an algebrotopological object (nontrivial only for mixed states) which captures the localisation of entanglement of the state. Particular examples of separabilty polytopes for 3partite systems
BOOLEAN FORMULAE, HYPERGRAPHS AND COMBINATORIAL TOPOLOGY
"... Abstract. With a view toward studying the homotopy type of spaces of Boolean formulae, we introduce a simplicial complex, called the theta complex, associated to any hypergraph. In particular, the set of satisfiable formulae in kconjunctive normal form with ≤ n variables has the homotopy type of Θ( ..."
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Cited by 2 (0 self)
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Abstract. With a view toward studying the homotopy type of spaces of Boolean formulae, we introduce a simplicial complex, called the theta complex, associated to any hypergraph. In particular, the set of satisfiable formulae in kconjunctive normal form with ≤ n variables has the homotopy type of Θ(Cube(n, n − k)), where Cube(n, n − k) is a hypergraph associated to the (n − k)skeleton of an ncube. We make partial progress in calculating the homotopy type of theta for these cubical hypergraphs, and we also give calculations and examples for other hypergraphs as well. Indeed studying the theta complex of hypergraphs is an interesting problem in its own right. 1.
Torus actions, combinatorial topology and homological algebra
 Michael W. Davis and Tadeusz Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus
, 1991
"... Abstract. The paper surveys some new results and open problems connected with such fundamental combinatorial concepts as polytopes, simplicial complexes, cubical complexes, and subspace arrangements. Particular attention is paid to the case of simplicial and cubical subdivisions of manifolds and, es ..."
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Cited by 11 (3 self)
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Abstract. The paper surveys some new results and open problems connected with such fundamental combinatorial concepts as polytopes, simplicial complexes, cubical complexes, and subspace arrangements. Particular attention is paid to the case of simplicial and cubical subdivisions of manifolds and
NONCOMMUTATIVE KOSZUL ALGEBRAS FROM COMBINATORIAL TOPOLOGY
, 811
"... Abstract. Associated to any uniform finite layered graph Γ there is a noncommutative graded quadratic algebra A(Γ) given by a construction due to Gelfand, Retakh, Serconek and Wilson. It is natural to ask when these algebras are Koszul. Unfortunately, a mistake in the literature states that all such ..."
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Cited by 6 (3 self)
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such algebras are Koszul. That is not the case and the theorem was recently retracted. We analyze the Koszul property of these algebras for two large classes of graphs associated to finite regular CW complexes, X. Our methods are primarily topological. We solve the Koszul problem by introducing new cohomology
Results 1  10
of
1,266