Residual deficiency and one relator quotients of triangle groups

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• Mariano Zeron-Medina
• Wednesday 31 October 2012, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Christopher Brookes.

In the first part of the talk, we define a real-valued invariant for finitely presented groups called residual deficiency. Given a finitely presented group G, its residual deficiency gives a lower bound for the deficiency of some finite index subgroups of G. Then we present some properties of the residual deficiency and show how it relates to already existing invariants which are used to study finitely presented infinite groups.

In the second part of the talk, we show a technique that helps estimate the residual deficiency of one relator quotients of triangle groups. This helps us conclude, under the right conditions, that some of these groups have finite index subgroups with deficiency greater than one, which as we will see, is a strong property.

This talk is part of the Algebra and Representation Theory Seminar series.

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