Algebraic combinatorics [electronic resource] : lectures at a summer school, Nordfjordeid, Norway, June, 2003 / Peter Orlik, Volkmar Welker.
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin ; London :
Springer,
2007.
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| Series: | Universitext.
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Table of Contents:
- PART I. LECTURES ON ARRANGEMENTS. Introduction
- 1. Algebraic combinatorics. Chamber counting. Ranking patterns. Random walks. The Orlik-Solomon algebra. The NBC complex. The Aomoto complex. Combinatorial types. Formal connections. Multiplicities. Ideal invariance. Examples. Exercises.
- 2. Applications. Topology. Local system cohomology. Resonance. Moduli spaces. Gauss-Manin connections. Exercises.
- References
- PART II. DISCRETE MORSE THEORY AND FREE RESOLUTIONS. 1. Introduction. Overview. Enumerative and algebraic invariants of simplicial complexes. Cohen-Macaulay simplicial complexes. Some open problems in the field
- 2. Basic definitions and examples. Multigraded free resolutions. Basics of CS-complexes. Basics of cellular homology. Cellular chain complexes and cellular resolutions. Co-Artinian monomial modules
- 3. Cellular resolution. When does a CS-complex support a cellular resolution? Reading off the Betti numbers. Examples of cellular resolutions
- 4. Discrete Morse theory. Forman's discrete Morse theory. Discrete Morse theory for graded CW-complexes. Minimizing cellular resolutions using discrete Morse theory. The Morse differential
- References
- Index.