English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The complement of a hyperplane arrangement in $\mathbb{C}^n$ deformationretracts onto an $n$-dimensional cell complex, but the known procedures onlyapply to complexifications of real arrangements (Salvetti) or the cell complexproduced depends on an initial choice of coordinates (Bj\"orner-Ziegler). Inthis article we consider the unique complex euclidean reflection group actingcocompactly by isometries on $\mathbb{C}^2$ whose linear part is the finitecomplex reflection group known as $G_4$ in the Shephard-Todd classification andwe construct a choice-free deformation retraction from its hyperplanecomplement onto an elegant $2$-dimensional complex $K$ where every $2$-cell isa euclidean equilateral triangle and every vertex link is a M\"obius-Kantorgraph. Since $K$ is non-positively curved, the corresponding braid group is aCAT(0) group, despite the fact that there are non-regular points in thehyperplane complement, the action of the reflection group on $K$ is not free,and the braid group is not torsion-free.

A complex euclidean reflection group with an elegant complement complex