Connectivity of the Gromov Boundary of the Free Factor Complex
Mladen Bestvina, Jon Chaika, Sebastian Hensel
TL;DR
This paper proves that for sufficiently large rank, the Gromov boundary of the free factor complex is both path connected and locally path connected, enhancing understanding of its topological structure.
Contribution
It establishes the path connectedness and local path connectedness of the Gromov boundary of the free factor complex in high rank cases.
Findings
Gromov boundary is path connected in large rank
Gromov boundary is locally path connected in large rank
Topological properties of the free factor complex boundary are clarified
Abstract
We show that in large enough rank, the Gromov boundary of the free factor complex is path connected and locally path connected.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology