Connectivity of partial basis complexes of freely decomposable groups

Key Points

• The research confirms that the complex of partial bases in free groups is Cohen–Macaulay.
• It shows that the dimension of these complexes aligns with theoretical predictions, satisfying a notable conjecture.
• The findings extend previous work beyond free groups, applying to a broader category of freely decomposable groups.
• The implications include deeper insights into the algebraic structure and connectivity properties of these mathematical entities.