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Abstract Mathematics teacher leaders may play an integral role in supporting change to address inequities in STEM education. To harness this potential, there is a need to identify effective professional development models that empower and motivate mathematics teacher leaders. We examine one such model focused on developing 30 K‐12 mathematics teacher leaders to support and expand teacher leadership within Nebraska, USA. Data analysis from interviews and surveys suggest that the project's focus on building and expanding teacher leaders' professional networks and increasing access to a variety of leadership opportunities contributed to a culture that empowered and motivated teacher leaders. Using the four frames model of organizational change in STEM, we identify several cultural features that contributed to the project's impact, including a cohort model connecting like‐minded educators that supported each other's efforts to enact changes; a distributed leadership philosophy that positioned participants as leaders within the project and at the university in which the project was situated; structural supports (e.g., funding, awards) for participants to engage in leadership; and a tailored approach to support participants based on their individual goals and vision for leadership. These findings have theoretical and practical implications for developing and supporting mathematics teacher leadership. 

Abstract The meridional rank conjecture asks whether the bridge number of a knot in$$S^3$$is equal to the minimal number of meridians needed to generate the fundamental group of its complement. In this paper, we investigate the analogous conjecture for knotted spheres in$$S^4$$. Towards this end, we give a construction to produce classical knots with quotients sending meridians to elements of any finite order in Coxeter groups and alternating groups, which detect their meridional ranks. We establish the equality of bridge number and meridional rank for these knots and knotted spheres obtained from them by twist-spinning. On the other hand, we show that the meridional rank of knotted spheres is not additive under connected sum, so that either bridge number also collapses, or meridional rank is not equal to bridge number for knotted spheres. 

Abstract We show that recent work of Song implies that torsion‐free hyperbolic groups with Gromov boundary arerealized as fundamental groups of closed 3‐manifolds of constant negative curvature if and only if the solution to an associated spherical Plateau problem for group homology is isometric to such a 3‐manifold, and suggest some related questions. 

In 2007, Cochran–Friedl–Teichner gave sufficient conditions for when a link obtained by multi-infection is topologically slice involving a Milnor’s invariant condition on the infecting string link. In this paper, we give a different Milnor’s invariant condition which can handle some cases which the original theorem cannot. Along the way, we also give sufficient conditions for a multi-infection to be [Formula: see text]-solvable, where we require that the infecting string link have vanishing pairwise linking numbers, which can be seen as handling an additional “[Formula: see text]-solvable” case of a well-known result about the relationship between satellite operations and the solvable filtration of Cochran–Orr–Teichner. 

We completely classify the locally finite, infinite graphs with pure mapping class groups admitting a coarsely bounded generating set. We also study algebraic properties of the pure mapping class group. We establish a semidirect product decomposition, compute first integral cohomology, and classify when they satisfy residual finiteness and the Tits alternative. These results provide a framework and some initial steps towards quasi-isometric and algebraic rigidity of these groups.