TY - JOUR
T1 - A descriptive construction of trees and stallings’ theorem
AU - Tserunyan, Anush
N1 - Funding Information:
The author’s research was partially supported by NSF Grant DMS-1501036.. I thank Institut Mittag-Leffler (Sweden) and the organizers of the program “Classification of Operator Algebras: Complexity, Rigidity, and Dynamics” in Spring of 2016 as the present research was done within this program at the institute. I am most grateful to Damien Gaboriau for encouraging this line of thought and for his feedback. I thank Martin Dunwoody and Dawid Kielak for pointing out various closely related papers and for helpful discussions. I also thank Clinton Conley, Andrew Marks, and Robin Tucker-Drob for going through my tree construction with me. Last but not least, many thanks to Vibeke Quorning for going through the paper with me and helping me discover some missing nontriviality assumptions in an earlier version of the current paper. Last but not least, I thank the anonymous referee for many useful suggestions and corrections, in particular, for pointing out the missing hypothesis of self-duality from Proposition 2.15 and onward.
Publisher Copyright:
© 2020 Anush Tserunyan.
PY - 2020
Y1 - 2020
N2 - We give a descriptive construction of trees for multi-ended graphs, which yields yet another proof of Stallings’ theorem on ends of groups. Even though our proof is, in principle, not very different from already existing proofs and it draws ideas from [Krö10] it is written in a way that easily adapts to the setting of countable Borel equivalence relations, leading to a free decomposition result and a sufficient condition for treeability.
AB - We give a descriptive construction of trees for multi-ended graphs, which yields yet another proof of Stallings’ theorem on ends of groups. Even though our proof is, in principle, not very different from already existing proofs and it draws ideas from [Krö10] it is written in a way that easily adapts to the setting of countable Borel equivalence relations, leading to a free decomposition result and a sufficient condition for treeability.
UR - http://www.scopus.com/inward/record.url?scp=85093884039&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85093884039&partnerID=8YFLogxK
U2 - 10.1090/conm/752/15137
DO - 10.1090/conm/752/15137
M3 - Article
AN - SCOPUS:85093884039
SN - 0271-4132
VL - 752
SP - 191
EP - 207
JO - Contemporary Mathematics
JF - Contemporary Mathematics
ER -