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math.GT2024
Topology of hyperplane arrangements via real structure
Masahiko Yoshinaga
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chamber…
math.GT2024
A construction of homotopically non-trivial embedded spheres for hyperplane arrangements
Masahiko Yoshinaga
We introduce the notion of locally consistent system of half-spaces for a real hyperplane arrangement. We embed a sphere in the complexified complement by shifting the real unit sp…
math.GT2024
-deformation of Aomoto complex
Masahiko Yoshinaga
A degree one element of the Orlik-Solomon algebra of a hyperplane arrangement defines a cochain complex known as the Aomoto complex. The Aomoto complex can be considerd as the ``li…