Arrangements of HyperplanesSpringer Science & Business Media, 2013年3月9日 - 325页 An arrangement of hyperplanes is a finite collection of codimension one affine subspaces in a finite dimensional vector space. Arrangements have emerged independently as important objects in various fields of mathematics such as combinatorics, braids, configuration spaces, representation theory, reflection groups, singularity theory, and in computer science and physics. This book is the first comprehensive study of the subject. It treats arrangements with methods from combinatorics, algebra, algebraic geometry, topology, and group actions. It emphasizes general techniques which illuminate the connections among the different aspects of the subject. Its main purpose is to lay the foundations of the theory. Consequently, it is essentially self-contained and proofs are provided. Nevertheless, there are several new results here. In particular, many theorems that were previously known only for central arrangements are proved here for the first time in completegenerality. The text provides the advanced graduate student entry into a vital and active area of research. The working mathematician will findthe book useful as a source of basic results of the theory, open problems, and a comprehensive bibliography of the subject. |
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第xiv页
... braid on three strands 160 5.2 A pure braid on three strands 160 • 5.3 The generator a¿ 5.4 K ( π , 1 ) , but not free 5.5 Three lines in general position 5.6 The critical half - line 5.7 Dual cells 5.8 Three concurrent lines in IR2 and ...
... braid on three strands 160 5.2 A pure braid on three strands 160 • 5.3 The generator a¿ 5.4 K ( π , 1 ) , but not free 5.5 Three lines in general position 5.6 The critical half - line 5.7 Dual cells 5.8 Three concurrent lines in IR2 and ...
第xv页
... ( 1 ) 222 6.2 The lattices L ( 12 ) , L ( 123 ) , ( 12 ) ( 34 ) . Ľ ( 1234 ) 222 " 6.3 The Hessian configuration 227 6.4 A tetrahedron in the cube 268 List of Tables 4.1 Induction table 4.2 The braid arrangement XVI List of Figures.
... ( 1 ) 222 6.2 The lattices L ( 12 ) , L ( 123 ) , ( 12 ) ( 34 ) . Ľ ( 1234 ) 222 " 6.3 The Hessian configuration 227 6.4 A tetrahedron in the cube 268 List of Tables 4.1 Induction table 4.2 The braid arrangement XVI List of Figures.
第xvi页
Peter Orlik, Hiroaki Terao. List of Tables 4.1 Induction table 4.2 The braid arrangement 5.1 A subspace arrangement 6.1 Poincaré polynomials 119 121 212 223 6.2 Restrictions 6.3 Orbits in G25 6.4 Induction table for G25 · 249 253 254 6.5 ...
Peter Orlik, Hiroaki Terao. List of Tables 4.1 Induction table 4.2 The braid arrangement 5.1 A subspace arrangement 6.1 Poincaré polynomials 119 121 212 223 6.2 Restrictions 6.3 Orbits in G25 6.4 Induction table for G25 · 249 253 254 6.5 ...
第2页
... braid space . The braid arrangement consists of the hyperplanes Hij ker ( zi Zj ) . Let M = { z € C2 | zi z ; for ij } be the complement of these hyperplanes , called the pure braid space . They proved that M is a K ( π , 1 ) space ...
... braid space . The braid arrangement consists of the hyperplanes Hij ker ( zi Zj ) . Let M = { z € C2 | zi z ; for ij } be the complement of these hyperplanes , called the pure braid space . They proved that M is a K ( π , 1 ) space ...
第3页
... braid arrangement by a finite Coxeter group W and its reflection representation in a real vector space VR of dimension l . Let V be the complexification of VR . Then W acts as a reflection group in V. Let Mw CV be the complement of the ...
... braid arrangement by a finite Coxeter group W and its reflection representation in a real vector space VR of dimension l . Let V be the complexification of VR . Then W acts as a reflection group in V. Let Mw CV be the complement of the ...
目录
1 | |
4 | |
15 | |
22 | |
Examples | 30 |
Algebras | 59 |
The Injective Map AAx AA | 65 |
Supersolvable Arrangements | 80 |
115 | 204 |
Reflection Arrangements | 215 |
A Some Commutative Algebra 271 | 270 |
B Basic Derivations | 279 |
Orbit Types | 289 |
ThreeDimensional Restrictions | 301 |
164 | 310 |
Index | 315 |
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A₁ affine arrangement algebra A(A arrangement and let assume b₁ basic derivations basic invariants basis for D(A bijection braid arrangement broken circuit called central arrangement choose cohomology complement complex reflection groups complexification compute Corollary Coxeter group defining polynomial Definition deformation retraction degree denote exact sequence Example exterior product fiber finite follows from Lemma follows from Proposition follows from Theorem formula free arrangement free with exp fundamental group G-orbit graph H₁ H₂ homogeneous homotopy type hyperplane arrangement inductively free integers irreducible isomorphism ker(x l-arrangement lattice Lemma Let G linear linearly independent Math matrix maximal element Möbius function modular elements nonempty Note Orbits Poincaré polynomial poset Proof prove real arrangement Recall reflection arrangement restriction result Section set of basic Shephard groups simplicial subset subspace supersolvable Suppose surjective topological unitary reflection group vertex w₁ write