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Seminar: "Labelled graphs and intersection of subgroups in fundamental groups of graphs of groups" (Alexander Zakharov, Universitat del Pais Basc)

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Seminari Teoria de Grups 2015/2016, session 13

Date: Tuesday May 24th, 2016, 13 - 14 h.
Place: FME-UPC room 101
Speaker: Alexander Zakharov (Universitat del Pais Basc)

Title: "Labelled graphs and intersection of subgroups in fundamental groups of graphs of groups"

 
Abstract: It is well-known that any finitely generated subgroup of a free group can be represented by a labelled graph in a good way by applying folding process, and this solves membership problem for free groups, and is very useful in general.
Intersection of two subgroups can be described in terms of these graphs also, and this allows to prove Howson's property, as well as Hanna Neumann inequality for subgroups of free groups.
 
This approach was generalized by Sergei Ivanov to free products in 1999, and then by Kapovich,Weidmann and Myasnikov to fundamental groups of graphs of groups in 2003. Under some conditions on the graph of groups they show how, given a finitely generated subgroup, one can construct a labelled graph representing this subgroup in a good way. They use generalized folding techniques. This allows to solve membership problem for some graphs of groups.
 
I will briefly survey the results and methods of Kapovich-Weidmann-Myasnikov and then show how we can apply (a modification of) their labelled graphs to study intersection of subgroups in some fundamental groups of graphs of groups, by using
"generalized pullback" of labelled graphs. This is joint work with Sergei Ivanov.

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