Arrangements of HyperplanesSpringer-Verlag, 1992 - 325页 |
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第191页
... exact sequences 0 → Hk + 1 ( M ( A ' ) ) → Hk + 1 ( M ( A ) ) → H * ( M ( A ′′ ) ) → 0 , and that this splitting ... exact sequence in de Rham cohomology . We give another elementary proof here , based on our work in the algebra R ...
... exact sequences 0 → Hk + 1 ( M ( A ' ) ) → Hk + 1 ( M ( A ) ) → H * ( M ( A ′′ ) ) → 0 , and that this splitting ... exact sequence in de Rham cohomology . We give another elementary proof here , based on our work in the algebra R ...
第192页
... exact sequence › H * ( M ' ) H * ( M ) H - 1 ( M " ) Hk + 1 ( M ' ) → where = T8 and 4 = j * T ̄1 . Proof . Consider the long exact sequence of the pair ( M ' , M ) in cohomology : → H * ( M ' ) → H * ( M ) & H * + 1 ( M ' , M ) ...
... exact sequence › H * ( M ' ) H * ( M ) H - 1 ( M " ) Hk + 1 ( M ' ) → where = T8 and 4 = j * T ̄1 . Proof . Consider the long exact sequence of the pair ( M ' , M ) in cohomology : → H * ( M ' ) → H * ( M ) & H * + 1 ( M ' , M ) ...
第194页
... exact sequence in Theorem 3.127 . Let K = Z. Lemma 5.86 There is a commutative diagram of exact sequences whose vertical maps n : R ( A ) → H * ( M ) are given by n ( WH ) = [ H ] : i - 0 Rk + 1 ( A ' ) Rk + 1 ( A ) → Rx ( A ...
... exact sequence in Theorem 3.127 . Let K = Z. Lemma 5.86 There is a commutative diagram of exact sequences whose vertical maps n : R ( A ) → H * ( M ) are given by n ( WH ) = [ H ] : i - 0 Rk + 1 ( A ' ) Rk + 1 ( A ) → Rx ( A ...
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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