| Description |
1 online resource (viii, 177 pages) : illustrations |
| Series |
Universitext |
|
Universitext.
|
| 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 |
| Summary |
Each year since 1996 the universities of Bergen, Oslo and Trondheim have organized summer schools in Nordfjordeid in various topics in algebra and related?elds. Nordfjordeid is the birthplace of Sophus Lie, and is a village on the western coast of Norway situated among fjords and mountains, with sp- tacularscenerywhereveryougo. AssuchitisawelcomeplaceforbothNor- gian and international participants and lecturers. The theme for the summer school in 2003 was Algebraic Combinatorics. The organizing committee c- sisted of Gunnar Fløystad and Stein Arild Strømme (Bergen), Geir Ellingsrud and Kristian Ranestad (Oslo), and Alexej Rudakov and Sverre Smalø (Tro- heim). The summer school was partly?nanced by NorFa-Nordisk Forsker- danningsakademi. With combinatorics reaching into and playing an important part of ever more areas in mathematics, in particular algebra, algebraic combinatorics was a timely theme. The?st lecture series "Hyperplane arrangements" was given by Peter Orlik. He came as a refugee to Norway, eighteen years old, after the insurrection in Hungary in 1956. Despite now having lived more than four decades in the United States, he impressed us by speaking?uent Norwegian without a trace of accent. The second lecture series "Discrete Morse theory and free resolutions" was given by Volkmar Welker. These two topics ori- nate back in the second half of the nineteenth century with simple problems on arrangements of lines in the plane and Hilberts syzygy theorem |
| Bibliography |
Includes bibliographical references (pages 169-172) and index |
| Notes |
English |
|
Print version record |
| In |
SpringerLink |
|
OhioLINK electronic book center |
| Subject |
Combinatorial geometry.
|
|
Free resolutions (Algebra)
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|
Combinatorial geometry
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Free resolutions (Algebra)
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| Form |
Electronic book
|
| Author |
Welker, Volkmar.
|
| ISBN |
3540683763 |
|
3540683755 |
|
9783540683759 |
|
9783540683766 |
|
