Mark Sapir: On subgroups of the R. Thompson group F скачать в хорошем качестве

Mark Sapir: On subgroups of the R. Thompson group F

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: Chapter markers and keywords to watch the parts of your choice in the video Videos enriched with abstracts, bibliographies, Mathematics Subject Classification Multi-criteria search by author, title, tags, mathematical area We provide two ways to show that the R. Thompson group F has maximal subgroups of infinite index which do not fix any number in the unit interval under the natural action of F on (0,1), thus solving a problem by D. Savchuk. The first way employs Jones' subgroup of the R. Thompson group F and leads to an explicit finitely generated example. The second way employs directed 2-complexes and 2-dimensional analogs of Stallings' core graphs, and gives many implicit examples. We also show that F has a decreasing sequence of finitely generated subgroups F [is greater than] H1 [is greater than] H2 [is greater than]... such that ∩Hi=1 and for every i there exist only finitely many subgroups of F containing Hi. Recording during the thematic meeting: "GAGTA-9 : Geometric, asymptotic and combinatorial group theory and applications" the September 15, 2015 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Pascal Vichi