Poset Topology: Tools and Applications
نویسنده
چکیده
Contents Poset Topology: Tools and Applications 1 Introduction 3 Lecture 1. Basic definitions, results, and examples 5 1.1. Order complexes and face posets 5 1.2. The Möbius function 9 1.3. Hyperplane and subspace arrangements 11 1.4. Some connections with graphs, groups and lattices 16 1.5. Poset homology and cohomology 17 1.6. Top cohomology of the partition lattice 19 Lecture 2. Group actions on posets 23 2.1. Group representations 23 2.2. Representations of the symmetric group 25 2.3. Group actions on poset (co)homology 30 2.4. Symmetric functions, plethysm, and wreath product modules 32 Lecture 3. Shellability and edge labelings 41 3.
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