Virtual retractions in graphs of groups and applications

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• Ashot Minasyan (University of Southampton)
• Wednesday 03 September 2025, 11:45-12:45
• Seminar Room 1, Newton Institute.

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OGGW02 - Actions on graphs and metric spaces

A subgroup H of a group G is a virtual retract if H is a retract of a finite index subgroup K in G, that is, H

A group has property (VRC) if every cyclic subgroup is a virtual retract. Examples of groups satisfying this property include virtually special groups (in the sense of Haglund and Wise), and, more generally, RFRS groups (in the sense of Agol).

 

In the talk I will discuss necessary and sufficient criteria for G to have (VRC), where G is the fundamental group of a finite graph of groups. In the case when the vertex groups are virtually abelian these criteria can be checked using elementary tools from Linear Algebra and Euclidean Geometry. I will also discuss applications of (VRC) to algebraic and geometric properties of G.

 

The talk will be based on recent joint work with Jon Merladet

   

This talk is part of the Isaac Newton Institute Seminar Series series.

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