TL;DR
This paper introduces a geometric characterization of the spine of untwisted outer space for right-angled Artin groups, realized through a new class of locally CAT(0) cube complexes based on spatial cube complexes.
Contribution
It provides a novel geometric framework for understanding the spine of outer space using spatial cube complexes, linking group theory and geometric topology.
Findings
New geometric characterization of the spine of outer space.
Construction of a new class of locally CAT(0) cube complexes.
Simplified definition via hyperplane collapses.
Abstract
We provide a new geometric characterization for the spine of untwisted outer space of a right-angled Artin group, constructed by Charney, Stambaugh, and Vogtmann. We realize the spine as the natural simplicial complex associated with the category of spatial cube complexes, a new class of locally CAT(0) cube complexes with a simple definition in terms of hyperplane collapses.
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Taxonomy
TopicsDigital Image Processing Techniques · Genome Rearrangement Algorithms · Data Management and Algorithms