Geometric Group Therapy Seminar

Speaker: Agustín Barreto

Title: The non-positive immersion property for generalized Wirtinger presentations

Abstract: In the last decades, locally indicable groups have emerged in many works related to known problems in topology, algebra, and geometry. These groups are characterized by the property that every non-trivial finitely generated subgroup admits an epimorphism onto the integers. In particular, they appear in problems concerning asphericity, orderability, and equations over groups.

In the early 2000s, Wise introduced a topological variant of non-positive curvature for 2-complexes: the non-positive immersion property. This notion is closely related to local indicability and is also used to study the coherence and cohomological properties of the fundamental groups of 2-complexes. Recently, this concept has regained relevance due to its deep connection with Bausmlag's conjecture, which was recently proven by A. Jaikin-Zapirain and M. Linton.

In this talk, I will present new methods, developed in joint work with Gabriel Minian, to study the local indicability of groups that admit generalized Wirtinger presentations. We then apply our methods to study the non-positive immersion property for the 2-complexes associated to these presentations. This provides a large family of concrete examples of 2-complexes (which can be described algorithmically) with the non-positive immersion property.

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