Orderable Groups September 1 to 5, 2014
Cajón del Maipo, RM, ChileIn this meeting, we will focus on many aspects concerning Orderable Groups and the relations (among others) with Geometric Group Theory, Low Dimensional Topology, and Dynamics. The idea is to gather around 40 people from different subjects in order to promote discussion and collaboration. There will be three minicourses, as well as a few (mostly informal) talks.
Local expenses of all the participants will be covered by the organizers.
We hope seeing you at «Cajón del Maipo» !
Minicourses:
1) Ordered groups and topology.
Adam Clay (U. Québec / Montréal).
2) Orderable group actions and the deepfall property.
Igor Mineyev (Illinois Univ. at Urbana Champaign).
3) Spaces of orderings,
Andrés Navas (USACH), Cristóbal Rivas (USACH), and Tetsuya Ito (U. Kyoto).
4) Orderable groups and dynamics,
Bertrand Deroin (ENS Paris, CNRS).
Juan Alonso, Univ. de la República, Uruguay.
Diego Arcis, Univ. de Bourgogne, Dijon, France.
Marcos Barrios, Univ. de la República, Uruguay.
Collin Bleak*, Univ. St Andrews, Scotland.
Michel Boileau*, Univ. Paul Sabatier, Toulouse, France.
Steven Boyer, Univ. du Québec à Montréal, Canada.
Joaquín Brun, Univ. de la República, Uruguay.
Danny Calegari*, Univ. of Chicago, USA.
Matthieu Calvez, Univ. de Santiago, Chile.
Carolina Canales, Univ. d´Orsay, France.
Gonzalo Castro, Univ. de Santiago, Chile.
Paulina Cecchi, Univ. de Chile.
Adam Clay, Univ. of Manitoba, Canada.
Patrick Dehornoy*, Univ. de Caen, France.
Bertrand Deroin, ENS Paris, France.
Mahdi Teymuri Garakani, Univ. de Santiago, Chile.
Natalia González, Univ. de Chile.
Juan González Meneses, Universidad de Sevilla, Spain.
Cameron Gordon, Univ. of Texas at Austin, USA.
Nancy Guelman, Univ. de la República, Uruguay.
Tetsuya Ito, Univ. of Kyoto, Japan.
Eduardo Jorquera, Pont. Univ. Católica de Valparaíso, Chile.
Dawid Kielak, Univ. Bonn, Germany.
Nicolás Libedinsky, Univ. de Chile.
Lucy Lifschitz*, Univ. of Oklahoma, USA.
Peter Linnell*, Virginia Tech. Blacksburg, USA.
Yash Lodha, Cornell Univ., USA.
Patrizia Longobardi*, Univ. degli studi di Salermo, Italy.
Jérôme Los, Univ. de Provence, France.
Mercede Maj*, Univ. degli studi di Salermo, Italy.
Yoshifumi Matsuda, Aoyama Gakuin University, Japan.
Igor Mineyev, Univ. Illinois at UrbanaChampaigne, USA.
Nicolas Monod*, É. Polytechnique Féd. de Lausanne, Switzerland.
Ignacio Monteverde, Univ. de la República, Uruguay.
Dave Morris, Univ. of Lethbridge, Canada.
Andrés Navas, Univ. de Santiago, Chile.
Pamela Pastén, Univ. de Chile.
Luis Paris, Univ. de Bourgogne, Dijon, France.
José Luis Pérez, Univ. de Santiago, Chile.
Yago Antolín Pichel, Vanderbilt Univ., Nashville, USA.
Fermín Reveles, CIMAT, México.
Cristóbal Rivas, Univ. de Santiago, Chile.
Rachel Roberts, Washington Univ., USA.
Dale Rolfsen*, Univ. British Columbia, Canada.
Zoran Sunic, Texas A&M Univ., College Station, USA.
Alexey Talambutsa, Univ. of Geneva, Switzerland.
Romain Tessera*, Univ. d´Orsay, France.
Aníbal Velozo, Princeton Univ., USA.
Andrea Vera, Univ. de Santiago, Chile.
Alden Walker, Univ. of Chicago, USA.
M T W T F S
08 00 – 09 00 

breakfast 
breakfast 
breakfast 
breakfast 
breakfast 
09 00 – 09 50 
breakfast  Deroin  Deroin  Ito  Los  informal talks 
10 00 – 10 50 
MorrisWitte  Clay  Clay  Clay  Mineyev  informal talks 
10 50 – 11 20 
cofee  cofee  cofee  cofee  cofee  farewell 
11 20 – 12 10 
Deroin  Rivas  Mineyev  Roberts  Lodha  
12 10 – 14 30 
lunch  lunch  lunch  lunch  lunch  
14 30 – 15 20 
Navas  Kielak  free  Gordon  AntolínPichel  
15 30 – 16 20 
Longobardi  Sunic  free  Boyer  TBA  
16 20 – 17 00 
cofee  cofee  free  cofee  cofee  
17 00 – 17 50 
Walker  Mineyev  free 
problems session 
problems session 

20 00 – 22 00 
dinner  dinner  dinner  dinner  dinner 
The conference will be held at the lodge «Cascada de las Ánimas» www.cascadadelasanimas.cl at Cajón del Maipo, a beautiful landscape on the hillside of the Andes Mountains, 1 hour away from Santiago de Chile.
The organizers will take care of all participants transportation from Santiago´s airport (on Sunday 31 August) to the place of the conference and back (on Saturday 06 by noon). The lodging of all participants is also covered by the organization, including meals and coffee breaks from Monday to Saturday morning.
Besides this, the lodge counts with activities like rafting, canopy, horse back riding, massages. Cascada accepts credit cards, but does not have an ATM. Therefore, if you would like to go around and get to know more of Cajón del Maipo, you will need to get some local currency in the airport. Cascada also has a SUV for rent. There is an ATM in the village of San José de Maipo, which is 10 minutes away by car or public transportation.
Weather in September (the beginning of the spring) in this part of Chile is cold in the mornings (510°C) and then the temperature goes up 1520°C in the afternoon, so bring your jacket and boots, and maybe an umbrella, because there is always the possibility of rain.
In case of problems upon your arrival, you can contact us to the phone number 56 9 74845109.
Last but not least, if you are entering to Chile with a passport issued by Australia, Canada, México, or USA, you have to pay a Reciprocity Tax at the airport; please check: www.aeropuertosantiago.cl/english/index.php?option=com_content&id=35&task=view&Itemid=51
We are looking forward to see you in September.
TALKS 

Name 
Yago Antolin Pichel 
Institution 
Vanderbilt University 
Title 
Local indicability and onerelator structures. 

Abstract 
In this talk I will review some classical theorems about local indicability for onerelator quotients and an approach to them via BassSerre Theory. 

Name 
Steven Boyer 
Institution 
Université du Québec `a Montréal 
Title 
Foliations, orders, representations, Lspaces and graph manifolds 

Abstract 
Much work has been devoted in recent years to examining relationships between the existence of a cooriented taut foliation in a closed, connected, prime 3manifold W, the leftorderability of the fundamental group of W, and the property that W not be a HeegaardFloer Lspace. When W has a positive first Betti number, each of these conditions holds. If W is a nonhyperbolic geometric manifold the conditions are known to be equivalent. In this talk I will discuss joint work with Adam Clay concerning the case that W is a graph manifold rational homology 3sphere. We show that W has a leftorderable fundamental group if and ony if it admits a cooriented taut foliation and show that these conditions imply that W is not an Lspace. 

Name 
Cameron Gordon 
Institution 
The University of Texas at Austin 
Title 
Leftorderability and cyclic branched covers 

Abstract 
It is conceivable that for a prime rational homology 3sphere M, the following conditions are equivalent: (1) pi_1(M) is leftorderable, (2) M admits a coorientable taut foliation, and (3) M is not a Heegaard Floer homology Lspace. We will discuss these properties in the case where M is the cyclic branched cover of a knot. This is joint work with Tye Lidman. 

Name 
Dawid Kielak 
Institution 
Universität Bonn 
Title 
Groups with infinitely many ends and fractions 

Abstract 
We will investigate some obstructions of a topological nature which prohibit a group from being a fraction group of a finitely generated subsemigroup. We will then apply our investigation to free groups and obtain two applications: we will see that free groups do not admit isolated orderings nor finite Garside structures. 

Name 
Yash Lodha 
Institution 
Cornell University, USA 
Title 
A geometric solution to the von NeumannDay problem for finitely presented groups. 

Abstract 
We will describe a finitely presented group of homeomorphisms of the circle that is nonamenable and does not contain nonabelian free subgroups. 



Name 
Patrizia Longobardi 
Institution 
Università degli studi di Salerno 
Title 
Some results on small doubling in ordered groups 

Abstract 
A finite subset S of a group G is said to satisfy the small doubling 

Name 
Jérôme Los 
Institution 
Université de Provence 
Title 
A formula for volume entropy of classical presentations for all surface groups 

Abstract 
Using dynamical system arguments we prove an explicit formula to compute the volume entropy of all surface groups for the classical presentations. 

Name 
Dave Morris 
Institution 
University of Lathbridge 
Title 
Survey of invariant orders on arithmetic groups 

Abstract 
At present, there are more questions than answers about the existence of an invariant order on an arithmetic group. We will discuss four different versions of the problem: the order may be required to be total, or allowed to be only partial, and the order may be required to be invariant under multiplication on both sides, or only on one side. One version is trivial, but the other three are related to interesting conjectures in the theory of arithmetic groups. 

Name 
Rachel Roberts 
Institution 
Washington University 
Title 
The LiRoberts Conjecture 

Abstract 
Suppose M is an irreducible, rational homology sphere. I will describe work, joint with Tao Li, in which we establish the 

Name 
Zoran Sunic 
Institution 
Texas A&M University 
Title 
Ordering free groups and free products. 

Abstract 
We utilize a criterion for the existence of a free subgroup acting freely on at least one of its orbits to construct such actions of the free group on the circle and on the line, leading to orders on free groups that are particularly easy to state and work with. We then switch to a restatement of the orders in terms of certain quasicharacters of free groups, from which properties of the defined orders may be deduced (some have positive cones that are contextfree, some have word reversible cones, some of the orders extend the usual lexicographic order, and so on). Finally, we construct total orders on the vertex set of an oriented tree. The orders are based only on updown counts at the interior vertices and the edges along the unique geodesic from a given vertex to another. As an application, we provide a short proof of Vinogradov´s result that the free product of leftorderable groups is leftorderable. 

Name 
Alden Walker 
Institution 
University of Chicago 
Title 
Transfers of quasimorphisms 

Abstract 
Let F be a free group. I´ll describe a transfer construction which lifts the rotation number quasimorphism from a finite index subgroup of F to F, and I´ll give a combinatorial explanation of when such a construction can be extremal for a given word in the free group. This is joint work with Danny Calegari. 



MINICOURSES 

Name 
Adam Clay 
Institution 
University of Manitoba, Canada 
Minicourse 
Orderable groups and topology 

Abstract 
The goal of this minicourse is to study the orderability properties of fundamental groups of 3manifolds, and when possible, explain orderability or nonorderability of the fundamental group via topological properties of the manifold. In particular I will cover biorderability of knot groups, connections with foliations, group actions and the Lspace conjecture; the lectures will include plenty of open problems and conjectures that are active areas of research. Owing to a theorem of Boyer, Rolfsen and Wiest (to be covered in the first lecture), this material is naturally best organized into two cases: The case of infinite first homology, and the case when the first homology is finite. The lectures will therefore cover material as follows: Lecture 1: The case of infinite first homology. Lectures 2 and 3: The case of finite first homology. References: Notes and a list of references will be available for each talk. 

Name 
Igor Mineyev 
Institution 
Univ. Illinois at UrbanaChampaigne, USA 
Minicourse 
Orderable group actions and the deepfall property. 

Abstract 
The above title is intensionally misleading: “orderable” can be either a 

Name 
Bertrand Deroin 
Institution 
Université ParisSud Faculté des Sciences d´Orsay 
Title 
Orderable groups and dynamics 

Abstract 
The lectures will focus on the dynamics of countable groups acting faithfully on the real line by preserving orientation homeomorphisms. As is wellknown, those groups are precisely the countable groups that admit a leftorder. The first part will be dedicated to the study of contraction properties of such actions, with applications to the problem of existence of a free subgroup, and the second will discuss the notion of almostperiodic actions, among them being the interesting harmonic ones. A nice object coming out here is a compact one dimensional foliated space, namely the space of almostperiodic actions (resp. the space of normalized harmonic ones), which can serve as a substitute to the space of leftorders (this latter will be discussed in the minicourse by Navas/Rivas/Ito/Paris). Dynamical properties of this foliation, as for instance the existence of periodic orbits, fixed points, invariant measures etc.. reveal some interesting properties of the algebraic structure of the group, as we will try to explain. 

Name 
Tetsatoya Ito 
Institution 
Research Institute for Mathematical Sciences, Kyoto University 
Title 
Constructing isolated orderings 

Abstract 
An isolated ordering, though its definition is easy, is not easy to find 

Name 
Andrés Navas 
Institution 
Universidad de Santiagode Chile 
Title 
Spaces of leftorderings. 

Abstract 
The space of orders of a group was introduced by Ghys and independently by Sikora. In general, this is a totally disconnected compact space upon which the group acts by conjugacy; moreover, for countable groups, it is metrizable. 

Name 
Cristóbal Rivas 
Institution 
Universidad de Santiagode Chile 
Title 
On the space of leftorderings of virtually solvable groups 

Abstract 
A general strategy for trying to approximate a leftordering on a group, is to approximate the given ordering by its conjugates. For instance, Navas has shown that this strategy always works unless the Conradian Soul of the initial ordering is a group admitting only finitely many leftorderings. 