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Boolean formulae, hypergraphs and combinatorial topology
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, which is the Alexander dual ofExpand
Seiberg-Witten Invariants, Alexander Polynomials, and Fibred Classes
Since their introduction in 1994, the Seiberg-Witten invariants have becomeone of the main tools used in 4-manifold theory. In this thesis, we will use these invariantsto identify sufficientExpand
A Study of the Homology of Subset Spaces and their Connection to the K-SAT Problem in Computer Science
It is the purpose of this thesis to introduce an idea for studying questions of computer science via topology. Expand