scholarly journals Volume rigidity ad ideal points of the character variety of hyperbolic 3-manifolds

2020 ◽  
Vol 20 (4) ◽  
pp. 1325-1344 ◽  
Author(s):  
Stefano Francaviglia ◽  
Alessio Savin
Keyword(s):  
Character Variety ◽  
Ideal Points ◽  
Volume Rigidity

scholarly journals A METHOD TO FIND IDEAL POINTS FROM IDEAL TRIANGULATIONS

2010 ◽  
Vol 19 (04) ◽  
pp. 509-524
Author(s):  
YUICHI KABAYA
Keyword(s):  
Linear Algebra ◽  
Character Variety ◽  
Ideal Triangulations ◽  
Ideal Points

We give a method to find ideal points of the character variety of a 3-manifold with toral boundary. This can be easily carried out by using linear algebra.

scholarly journals Conway spheres as ideal points of the character variety

2011 ◽  
Vol 354 (2) ◽  
pp. 707-726
Author(s):  
Luisa Paoluzzi ◽  
Joan Porti
Keyword(s):  
Character Variety ◽  
Ideal Points

Toric Geometry ofSL2(ℂ) Free Group Character Varieties from Outer Space

2018 ◽  
Vol 70 (2) ◽  
pp. 354-399 ◽  
Author(s):  
Christopher Manon
Keyword(s):  
Free Group ◽  
Outer Space ◽  
Integrable Hamiltonian System ◽  
Outer Automorphism ◽  
Character Variety ◽  
Toric Geometry ◽  
Character Varieties ◽  
Simplicial Space ◽  
Proper Map ◽  
Divisorial Valuations

AbstractCuller and Vogtmann defined a simplicial spaceO(g), calledouter space, to study the outer automorphism group of the free groupFg. Using representation theoretic methods, we give an embedding ofO(g) into the analytification of X(Fg,SL2(ℂ)), theSL2(ℂ) character variety ofFg, reproving a result of Morgan and Shalen. Then we show that every pointvcontained in a maximal cell ofO(g) defines a flat degeneration of X(Fg,SL2(ℂ)) to a toric varietyX(PΓ). We relate X(Fg,SL2(ℂ)) andX(v) topologically by showing that there is a surjective, continuous, proper map Ξv:X(Fg,SL2(ℂ)) →X(v). We then show that this map is a symplectomorphism on a dense open subset of X(Fg, SL2(ℂ)) with respect to natural symplectic structures on X(Fg, SL2(ℂ)) andX(v). In this way, we construct an integrable Hamiltonian system in X(Fg, SL2(ℂ)) for each point in a maximal cell ofO(g), and we show that eachvdefines a topological decomposition of X(Fg, SL2(ℂ)) derived from the decomposition ofX(PΓ) by its torus orbits. Finally, we show that the valuations coming from the closure of a maximal cell inO(g) all arise as divisorial valuations built from an associated projective compactification of X(Fg, SL2(ℂ)).

scholarly journals When National Unity Governments are neither National, United, nor Governments: The Case of Tunisia

2018 ◽  
Author(s):  
Robert Kubinec ◽  
Sharan Grewal
Keyword(s):  
Political Parties ◽  
Ideal Point ◽  
Power Sharing ◽  
Government Performance ◽  
Success Story ◽  
National Unity ◽  
Longitudinal Survey Data ◽  
Transitional Democracies ◽  
Ideal Points ◽  
The Cost

Is power-sharing an effective way for endangered transitional democracies to reduce political tensions and improve government performance? We provide one of the first quantitative tests of this question in Tunisia, the Arab Spring's only success story. We argue that power-sharing may reduce polarization for a limited time, but at the cost of undermining democratic institutions. To measure polarization, we examine all rollcall votes from Tunisia's first and second post-transition parliaments. We employ a time-varying ideal point model and examine whether power-sharing agreements led to convergence in political parties' ideal points. Our analysis reveals that Tunisia's national unity government in 2015 temporarily moderated political tensions and allowed for parliamentary activity to resume. However, despite a broadening of the coalition in mid-2016, polarization reemerged and crucial legislation stalled. Moreover, longitudinal survey data suggest that the failure of power-sharing in Tunisia contributed to disillusionment with political parties, parliament, and democracy.

A Socioeconomic Comparison of Turkey vs. Participating Countries in the Fifth and Sixth Waves of European Union Enlargement

2020 ◽  
pp. 117-132
Author(s):  
İbrahim Akbulut ◽  
Nezih Tayyar ◽  
Koray Yapa ◽  
Mert Durmus
Keyword(s):  
European Union ◽  
Economic Indicators ◽  
The European Union ◽  
European Union Enlargement ◽  
Social And Economic Development ◽  
European Union Countries ◽  
Ideal Points ◽  
Mcdm Method ◽  
Education Culture ◽  
Ideal Method

Many social and economic variables are used as indicators of the level of development of countries. To determine the level of social and economic development, many criteria were studied in the fields of education, culture, health, and economy. This chapter analyzes 13 European Union countries that participated in the fifth and sixth enlargement process and Turkey, whose ongoing process of accession to the European Union is determined by using socio-economic indicators. Reference Ideal Method (RIM) is a new Multi Criteria Decision Making (MCDM) method. This method differentiates itself from other methods frequently used in literature by using the ideal points or ideal ranges. The chapter shows Turkey must improve socio-economic indicators to be close to the countries in the fifth and sixth waves of enlargement process of European Union.

Global Ideological Conflict

2021 ◽  
pp. 17-40
Author(s):  
Erik Voeten
Keyword(s):  
United Nations ◽  
Regime Type ◽  
General Assembly ◽  
Policy Positions ◽  
United Nations General ◽  
Government Ideology ◽  
Institutional Politics ◽  
Ideal Points ◽  
United Nations General Assembly ◽  
Definition Of

This chapter discusses the definition of institutions and then of ideology. Ideology is a set of widely understood more or less cohesive and stable ideas about how a set of issues should be resolved and who should resolve them. It is a vehicle not just for spreading values but also for transmitting information. This information is especially valuable in contexts where actors care deeply about the future intentions of others, including international institutional politics. The chapter then assesses how this definition differs from other treatments in the international relations literature, how ideology constrains policy positions, and what global ideological debates are about. It also outlines an approach to estimate the ideological positions of states from votes in the United Nations General Assembly (UNGA). It evaluates the validity of this measure. For example, changes in UNGA ideal points correlate strongly with various indicators of liberalism: such as changes in government ideology, regime type, and capital openness.

scholarly journals Quantum computing and the brain: quantum nets, dessins d’enfants and neural networks

2019 ◽  
Vol 198 ◽  
pp. 00014
Author(s):  
Torsten Asselmeyer-Maluga
Keyword(s):  
Neural Networks ◽  
Quantum Computing ◽  
Feedback Loops ◽  
Character Variety ◽  
General Transformation ◽  
Closed Loops ◽  
Dessins D’Enfants ◽  
Topological Quantum ◽  
The Neural Network ◽  
Dessins D'enfants

In this paper, we will discuss a formal link between neural networks and quantum computing. For that purpose we will present a simple model for the description of the neural network by forming sub-graphs of the whole network with the same or a similar state. We will describe the interaction between these areas by closed loops, the feedback loops. The change of the graph is given by the deformations of the loops. This fact can be mathematically formalized by the fundamental group of the graph. Furthermore the neuron has two basic states |0〉 (ground state) and |1〉 (excited state). The whole state of an area of neurons is the linear combination of the two basic state with complex coefficients representing the signals (with 3 Parameters: amplitude, frequency and phase) along the neurons. If something changed in this area, we need a transformation which will preserve this general form of a state (mathematically, this transformation must be an element of the group S L(2; C)). The same argumentation must be true for the feedback loops, i.e. a general transformation of states along the feedback loops is an assignment of this loop to an element of the transformation group. Then it can be shown that the set of all signals forms a manifold (character variety) and all properties of the network must be encoded in this manifold. In the paper, we will discuss how to interpret learning and intuition in this model. Using the Morgan-Shalen compactification, the limit for signals with large amplitude can be analyzed by using quasi-Fuchsian groups as represented by dessins d’enfants (graphs to analyze Riemannian surfaces). As shown by Planat and collaborators, these dessins d’enfants are a direct bridge to (topological) quantum computing with permutation groups. The normalization of the signal reduces to the group S U(2) and the whole model to a quantum network. Then we have a direct connection to quantum circuits. This network can be transformed into operations on tensor networks. Formally we will obtain a link between machine learning and Quantum computing.

scholarly journals Maximal metric surfaces and the Sobolev-to-Lipschitz property

2020 ◽  
Vol 59 (5) ◽  
Author(s):  
Paul Creutz ◽  
Elefterios Soultanis
Keyword(s):  
Metric Spaces ◽  
Equivalence Classes ◽  
Plateau Problem ◽  
Lipschitz Property ◽  
Maximality Condition ◽  
Volume Rigidity

Abstract We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated notions of Sobolev-to-Lipschitz property, or volume rigidity. We also apply our construction to solutions of the Plateau problem in metric spaces and obtain a variant of the associated intrinsic disc studied by Lytchak–Wenger, which satisfies a related maximality condition.

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