Arrangements of HyperplanesSpringer-Verlag, 1992 - 325页 |
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第39页
... formula determine μ recursively . The first known result which may be viewed as a precursor of the Möbius function appeared in the work of Euler . He started with the formula π2 6 1 1 1 1 1 1 = 1+ + + + + + + 22 32 42 52 62 and formally ...
... formula determine μ recursively . The first known result which may be viewed as a precursor of the Möbius function appeared in the work of Euler . He started with the formula π2 6 1 1 1 1 1 1 = 1+ + + + + + + 22 32 42 52 62 and formally ...
第205页
... formula is called the LCS ( lower central series ) formula . It connects the ranks of the successive quotients in the lower central series of the fundamental group of M with the Poincaré polynomial of M. It is natural to ask for the ...
... formula is called the LCS ( lower central series ) formula . It connects the ranks of the successive quotients in the lower central series of the fundamental group of M with the Poincaré polynomial of M. It is natural to ask for the ...
第220页
... formula says l - 2 l - 2 Σ ( -1 ) [ H1 ( F ) ] = Σ ( −1 ) [ C2 ( F ) ] q = 0 q = 0 where C1 ( F ) is the group of q - chains of F. From Theorem 4.106 and Proposition 6.12 , we get l - 2 Σ ( −1 ) o [ H , ( F ) ] = [ C ] + ( −1 ) ...
... formula says l - 2 l - 2 Σ ( -1 ) [ H1 ( F ) ] = Σ ( −1 ) [ C2 ( F ) ] q = 0 q = 0 where C1 ( F ) is the group of q - chains of F. From Theorem 4.106 and Proposition 6.12 , we get l - 2 Σ ( −1 ) o [ H , ( F ) ] = [ C ] + ( −1 ) ...
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常见术语和短语
A₁ affine arrangement algebra A(A arrangement and let assume b₁ basic derivations basic invariants basis for D(A braid arrangement broken circuit central arrangement chain complex choose cohomology complement complex reflection groups complexification compute Corollary Coxeter group defining polynomial Definition deformation retraction degree denote dependent exact sequence Example exterior algebra exterior product fiber finite follows from Lemma follows from Proposition follows from Theorem formula free arrangement free with exp G-orbit graded K-module graph H₁ H₂ homogeneous homotopy type hyperplanes inductively free integers irreducible isomorphism K-algebra ker(x l-arrangement lattice Lemma Let G linear linearly independent matrix maximal element Möbius function modular elements module N¹(A nonempty Note Orbits Poincaré polynomial poset Proof prove real arrangement Recall reflection arrangement restriction result Saito's criterion 4.19 Section Shephard groups simplicial subset subspace supersolvable supersolvable arrangement Suppose surjective vertex w₁ write x-independent