Incoherence of free-by-free and surface-by-free groups

Genevieve Walsh (Tufts University)

28-Apr-2020, 15:00-15:30 (4 years ago)

Abstract: A group is said to be coherent if every finitely generated subgroup is finitely presented. This property is enjoyed by free groups, and the fundamental groups of surfaces and 3-manifolds. A group that is not coherent is incoherent; it is very interesting to try and understand which groups have which property. We will discuss some of the geometric and topological aspects of this question, particularly quasi-convexity and algebraic fibres. We show that free-by-free and surface-by-free groups are incoherent, when the rank and genus are at least two.

This is joint work with Robert Kropholler and Stefano Vidussi.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( paper | slides )


Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start five minutes after the hour. Talks are typically 55 minutes long, including time for questions.

Organizers: Saul Schleimer*, Robert Kropholler*
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