Minimal stratifications for line arrangements and positive homogeneous presentations for fundamental groups

Yoshinaga, Masahiko

doi:10.1007/978-88-7642-431-1_22

Cited by 7 publications

(3 citation statements)

References 22 publications

(9 reference statements)

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“…The purpose of this paper is to develop a topological method of computing Milnor monodromy for complexified real arrangements following Cohen and Suciu. The new ingredient is a recent study of minimal cell structures for the complements of complexified real arrangements [19,22]. By using the description of twisted minimal chain complexes, we obtain an algorithm which computes monodromy eigenspaces directly from real figures without passing through the presentations of π 1 .…”

Section: Introductionmentioning

confidence: 99%

Milnor fibers of real line arrangements

Yoshinaga¹

2013

jsing

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We study Milnor fibers of complexified real line arrangements. We give a new algorithm computing monodromy eigenspaces of the first cohomology. The algorithm is based on the description of minimal CW-complexes homotopic to the complements, and uses the real figure, that is, the adjacency relations of chambers. It enables us to generalize a vanishing result of Libgober, give new upper-bounds and characterize the A 3 -arrangement in terms of non-triviality of Milnor

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Section: Introductionmentioning

confidence: 99%

Milnor fibers of real line arrangements

Yoshinaga¹

2013

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“…For further information about the fundamental groups of arrangements, see [19] and the references therein. Minimal stratifications of the complements of complexified real line arrangements had been studied by Yosihnaga in [24]. Recently, Sugawara and Yoshinaga gave Kirby diagrams for those arrangements using divides with cusps [25].…”

Section: Complexified Real Line Arrangementsmentioning

confidence: 99%

Presentation of the fundamental groups of complements of shadows

Ishikawa¹,

Koda²,

Naoe³

2021

Preprint

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A shadowed polyhedron is a simple polyhedron equipped with half integers on regions, called gleams, which represents a compact, oriented, smooth 4-manifold. The polyhedron is embedded in the 4-manifold and it is called a shadow of that manifold. A subpolyhedron of a shadow represents a possibly singular subsurface in the 4-manifold. In this paper, we focus on contractible shadows obtained from the unit disk by attaching annuli along generically immersed closed curves on the disk. In this case, the 4-manifold is always a 4-ball. Milnor fibers of plane curve singularities and complexified real line arrangements can be represented in this way. We give a presentation of the fundamental group of the complement of a subpolyhedron of such a shadow in the 4-ball. The method is very similar to the Wirtinger presentation of links in knot theory.

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“…The isomorphism (4) is natural in the sense that it respects Borel-Moore homology [27,14,28]. Recall that each chamber C ∈ ch 2…”

Section: Definition 42 We Use the Notations Above Considermentioning

confidence: 99%