scholarly journals Classification of the automorphism and isometry groups of Higgs bundle moduli spaces

2016 ◽  
Vol 112 (5) ◽  
pp. 827-854 ◽  
Author(s):  
D. Baraglia
Keyword(s):  
Moduli Spaces ◽  
Higgs Bundle ◽  
Isometry Groups

scholarly journals Involutions and higher order automorphisms of Higgs bundle moduli spaces

2019 ◽  
Vol 119 (3) ◽  
pp. 681-732 ◽  
Author(s):  
Oscar García‐Prada ◽  
S. Ramanan
Keyword(s):  
Moduli Spaces ◽  
Higher Order ◽  
Higgs Bundle

Classification of real moduli spaces over genus 2 curves

1995 ◽  
Vol 57 (2) ◽  
pp. 207-215 ◽  
Author(s):  
Shuguang Wang
Keyword(s):  
Moduli Spaces ◽  
Genus 2 ◽  
Genus 2 Curves

Classification of compact lorentzian 2-orbifolds with noncompact full isometry groups

2012 ◽  
Vol 53 (6) ◽  
pp. 1037-1050 ◽  
Author(s):  
N. I. Zhukova ◽  
E. A. Rogozhina
Keyword(s):  
Isometry Groups

Some Hyperbolic 3-Manifolds with Totally Geodesic Boundary

2010 ◽  
Vol 17 (03) ◽  
pp. 457-468 ◽  
Author(s):  
Agnese Ilaria Telloni
Keyword(s):  
Fundamental Groups ◽  
Isometry Groups ◽  
Geodesic Boundary ◽  
Totally Geodesic ◽  
Cyclic Coverings

We construct a family of compact hyperbolic 3-manifolds with totally geodesic boundary, depending on three integer parameters. Then we determine geometric presentations of the fundamental groups of these manifolds and prove that they are cyclic coverings of the 3-ball branched along a specified tangle with two components. Finally, we give a classification of these manifolds up to homeomorphism (resp., isometry), and determine their isometry groups.

Classification of U(1)-vortices with target ℂN

2015 ◽  
Vol 26 (13) ◽  
pp. 1550109 ◽  
Author(s):  
Guangbo Xu
Keyword(s):  
Complex Plane ◽  
Moduli Spaces ◽  
Finite Energy ◽  
Adiabatic Limit ◽  
Target Space ◽  
Vortex Equation ◽  
All Solutions

We study the symplectic vortex equation over the complex plane, for the target space [Formula: see text] ([Formula: see text]) with diagonal [Formula: see text]-action. Using adiabatic limit argument, we classify all solutions with finite energy and identify their moduli spaces, which generalizes Taubes’ result for [Formula: see text].

COHERENT SYSTEMS OF GENUS 0

2004 ◽  
Vol 15 (04) ◽  
pp. 409-424 ◽  
Author(s):  
H. LANGE ◽  
P. E. NEWSTEAD
Keyword(s):  
Moduli Spaces ◽  
Necessary Conditions ◽  
Projective Line ◽  
Coherent Systems

In this paper we begin the classification of coherent systems (E,V) on the projective line which are stable with respect to some value of a parameter α. In particular we show that the moduli spaces, if non-empty, are always smooth and irreducible of the expected dimension. We obtain necessary conditions for non-emptiness and, when dim V=1 or 2, we determine these conditions precisely. We also obtain partial results in some other cases.

Classifying C1+ structures on dynamical fractals: 2. Embedded trees

1995 ◽  
Vol 15 (5) ◽  
pp. 969-992 ◽  
Author(s):  
A. A. Pinto ◽  
D. A. Rand
Keyword(s):  
Moduli Spaces ◽  
Binary Tree ◽  
Conjugacy Classes ◽  
Expanding Maps ◽  
Bounded Geometry ◽  
Arbitrary Topology ◽  
Contact Points ◽  
Train Tracks ◽  
Smooth Conjugacy

AbstractWe classify the C1+α structures on embedded trees. This extends the results of Sullivan on embeddings of the binary tree to trees with arbitrary topology and to embeddings without bounded geometry and with contact points. We used these results in an earlier paper to describe the moduli spaces of smooth conjugacy classes of expanding maps and Markov maps on train tracks. In later papers we will use those results to do the same for pseudo-Anosov diffeomorphisms of surfaces. These results are also used in the classification of renormalisation limits of C1+α diffeomorphisms of the circle.

scholarly journals Polish Metric Spaces: Their Classification and Isometry Groups

2001 ◽  
Vol 7 (3) ◽  
pp. 361-375 ◽  
Author(s):  
John D. Clemens ◽  
Su Gao ◽  
Alexander S. Kechris
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Classification Problem ◽  
Classification Problems ◽  
Isometry Groups ◽  
Polish Spaces ◽  
Basic Ideas ◽  
In The Beginning ◽  
Theory Of Complexity

§ 1. Introduction. In this communication we present some recent results on the classification of Polish metric spaces up to isometry and on the isometry groups of Polish metric spaces. A Polish metric space is a complete separable metric space (X, d).Our first goal is to determine the exact complexity of the classification problem of general Polish metric spaces up to isometry. This work was motivated by a paper of Vershik [1998], where he remarks (in the beginning of Section 2): “The classification of Polish spaces up to isometry is an enormous task. More precisely, this classification is not ‘smooth’ in the modern terminology.” Our Theorem 2.1 below quantifies precisely the enormity of this task.After doing this, we turn to special classes of Polish metric spaces and investigate the classification problems associated with them. Note that these classification problems are in principle no more complicated than the general one above. However, the determination of their exact complexity is not necessarily easier.The investigation of the classification problems naturally leads to some interesting results on the groups of isometries of Polish metric spaces. We shall also present these results below.The rest of this section is devoted to an introduction of some basic ideas of a theory of complexity for classification problems, which will help to put our results in perspective. Detailed expositions of this general theory can be found, e.g., in Hjorth [2000], Kechris [1999], [2001].

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