Fundamental groups of partial compactifications of arrangements and homology planes

2021/09/08 by Rodolfo Aguilar, Aguilar, Rodolfo Aguilar
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2109.03593

openalex publication_date 2021/09/08 · openalex created_date 2021/09/13 · openalex updated_date 2026/07/28

Abstract

Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in particular, to homology planes arising from arrangements of lines. This permits to determine the infinitude of the fundamental group of homology planes of log-general type that may be the first examples of this type.

Citations

• Rational homology disk smoothings of surface singularities; the\n exceptional cases

Related

• The fundamental group of partial compactifications of the complement of a real line arrangement
• The fundamental group's structure of the complement of some configurations of real line arrangements
• Topology of plane arrangements and their complements
• Minimal stratifications for line arrangements and positive homogeneous presentations for fundamental groups
• Lectures on topology of complements and fundamental groups