This book is based on two series of lectures given at a summer school on algebraic combinatorics at the Sophus Lie Centre in Nordfjordeid, Norway, in June 2003, one by Peter Orlik on hyperplane arrangements, and the other one by Volkmar Welker on free resolutions. Both topics are essential parts of current research in a variety of mathematical fields, and the present book makes these sophisticated tools available for graduate students.
Recenzijos
From the reviews:
"This is really two books in one. It could be used by a weekly reading group by faculty and the occasional very advanced, talented and motivated student. it could be possibly be used for a special topics graduate course, for students who already had a graduate class in topology. This is because of its numerous exercises and its reader-friendly style." (Miklós Bóna, MathDL, May, 2007)
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Part I Lectures on Arrangements |
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5 | (8) |
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13 | (48) |
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13 | (4) |
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17 | (2) |
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19 | (4) |
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The Orlik-Solomon Algebra |
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23 | (4) |
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27 | (6) |
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33 | (7) |
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40 | (1) |
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41 | (2) |
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43 | (4) |
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47 | (5) |
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52 | (6) |
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58 | (3) |
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61 | (22) |
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61 | (3) |
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64 | (3) |
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67 | (1) |
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68 | (2) |
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70 | (6) |
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76 | (7) |
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77 | (6) |
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Part II Discrete Morse Theory and Free Resolutions |
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83 | (24) |
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83 | (2) |
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Enumerative and Algebraic Invariants of Simplicial Complexes |
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85 | (7) |
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Cohen-Macaulay Simplicial Complexes |
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92 | (5) |
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Some Open Problems in the Field |
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97 | (10) |
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Basic Definitions and Examples |
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107 | (18) |
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Multigraded Free Resolutions |
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107 | (6) |
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113 | (4) |
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Basics of Cellular Homology |
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117 | (3) |
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Cellular Chain Complexes and Cellular Resolutions |
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120 | (3) |
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Co-Artinian Monomial Modules |
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123 | (2) |
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125 | (20) |
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When Does a CW-Complex Support a Cellular Resolution? |
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125 | (3) |
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Reading off The Betti Numbers |
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128 | (3) |
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Examples of Cellular Resolutions |
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131 | (14) |
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145 | (28) |
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Forman's Discrete Morse Theory |
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146 | (2) |
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Discrete Morse Theory for Graded CW-Complexes |
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148 | (10) |
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Minimizing Cellular Resolutions using Discrete Morse Theory |
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158 | (1) |
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159 | (14) |
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169 | (4) |
| Index |
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173 | |
Orlik has been working in the area of arrangements for thirty years. Lectures on this subject include CBMS Lectures in Flagstaff, AZ; Swiss Seminar Lectures in Bern, Switzerland; and Summer School Lectures in Nordfjordeid, Norway, in addition to many invited lectures, including an AMS hour talk.
Welker works in algebraic and geometric combinatorics, discrete geometry and combinatorial commutative algebra. Lectures on the topic of the book include Summer School on Topological Combinatorics, Vienna and Summer School Lectures in Nordfjordeid, in addition to several invited talks.
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