Divides with cusps and Kirby diagrams for line arrangements

2021/03/29 by Sakumi Sugawara, Masahiko Yoshinaga, Sugawara, Sakumi +1
Engineering · Mathematics · #32Q55 #32S50 #52C35 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications #graph theory and CDMA systems #math.CO #math.GT #msc:32Q55 #msc:32S50 #msc:52C35

paper · pdf · doi:10.48550/arxiv.2103.15262

18 pages, 26 figures

openalex publication_date 2021/03/29 · arxiv created 2021/07/03 · arxiv updated 2021/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The complement of a complexified real line arrangement is an affine surface. It is classically known that such a space has a handle decomposition up to 2-handles. We will describe the handle decomposition induced from Lefschetz hyperplane section theorem for such a space. To describe the Kirby diagram, we introduce the notion of the divide with cusps which is a generalization of the divide introduced by A'Campo.

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