Fundamental Groups and Dendricity

The aim of the poster is to showcase the interplay between group theory, algebraic topology and combinatorics on words. A result that allows to display this is the return theorem by Berté et al. in 2015. The poster will contain an introduction to fundamental groups of graphs, dendric words as well as a new result concerning return groups of eventually dendric shifts.
More precisely, dendric words are words whose factors cannot be arbitrarily extended and their return groups are the groups of loops over their Rauzy graphs. These contain the structure of the entire word and so the specific structure induced by dendric words allows us to compute these groups explicitely.