Combinatorial Morse theory and minimality of hyperplane arrangements

نویسندگان
چکیده

منابع مشابه

Combinatorial Morse theory and minimality of hyperplane arrangements

In [DP03], [Ra02] it was proven that the complement to a hyperplane arrangement in C is a minimal space, i.e. it has the homotopy type of a CW -complex with exactly as many i-cells as the i-th Betti number bi. The arguments use (relative) Morse theory and Lefschetz type theorems. This result of ”existence” was refined in the case of complexified real arrangements in [Yo05]. The author consider ...

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Morse Theory, Milnor Fibers and Minimality of Hyperplane Arrangements

Through the study of Morse theory on the associated Milnor fiber, we show that complex hyperplane arrangement complements are minimal. That is, the complement of any complex hyperplane arrangement has the homotopy type of a CW-complex in which the number of p-cells equals the p-th betti number. Combining this result with recent work of Papadima and Suciu, one obtains a characterization of when ...

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Morse theory, Milnor fibers and hyperplane arrangements

Through the study of Morse theory on the associated Milnor fiber, we show that complex hyperplane arrangement complements are minimal. That is, the complement of any complex hyperplane arrangement has the homotopy type of a CW complex in which the number of p-cells equals the p-th betti number.

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Hyperplane arrangements and K-theory

Abstract. We study the Z2-equivariant K-theory of M(A), where M(A) is the complement of the complexification of a real hyperplane arrangement, and Z2 acts on M(A) by complex conjugation. We compute the rational equivariant K and KO rings of M(A), and we give two different combinatorial descriptions of a subring Line(A) of the integral equivariant KO ring, where Line(A) is defined to be the subr...

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A Combinatorial Reciprocity Theorem for Hyperplane Arrangements

Given a nonnegative integer m and a finite collection A of linear forms on Qd, the arrangement of affine hyperplanes in Qd defined by the equations α(x) = k for α ∈ A and integers k ∈ [−m,m] is denoted by Am. It is proved that the coefficients of the characteristic polynomial of Am are quasi-polynomials inm and that they satisfy a simple combinatorial reciprocity law.

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ژورنال

عنوان ژورنال: Geometry & Topology

سال: 2007

ISSN: 1364-0380,1465-3060

DOI: 10.2140/gt.2007.11.1733