Graphical C(3)-T(6) implies CAT(0)

TL;DR

This paper extends classical small cancellation theory to graphical complexes, demonstrating that graphical C(3)-T(6) complexes can be equipped with locally CAT(0) metrics, thus broadening the class of groups with such geometric structures.

Contribution

The paper introduces a method to construct locally CAT(0) metrics on graphical C(3)-T(6) complexes, generalizing classical results to a graphical setting.

Findings

Graphical C(3)-T(6) complexes admit locally CAT(0) metrics.

Extension of classical small cancellation results to graphical complexes.

Provides new tools for constructing groups with CAT(0) properties.

Abstract

Graphical small cancellation extends the classical small cancellation theory and provides a powerful method for constructing groups with interesting features. In the classical setting, C(3)-T(6) small cancellation complexes are known to admit locally CAT(0) metrics. In this paper, we construct locally CAT(0) metrics for graphical C(3)-T(6) complexes.