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Computing and Understanding Representation Varieties Efficiently

Identify the representations that correspond to geometric structures. A PGL(2,C)-representation corresponds to a hyperbolic structure if all shapes have positive imaginary part. There should be a similar condition for spherical CR-structures and real flag structures. Understand the mysterious duality between the shape and Ptolemy coordinates. Generalize the shape and Ptolemy coordinates to other Lie-groups and higher dimensional manifolds.

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Computing and Understanding Representation Varieties Efficiently | curve.unhyperbolic.org Reviews

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Identify the representations that correspond to geometric structures. A PGL(2,C)-representation corresponds to a hyperbolic structure if all shapes have positive imaginary part. There should be a similar condition for spherical CR-structures and real flag structures. Understand the mysterious duality between the shape and Ptolemy coordinates. Generalize the shape and Ptolemy coordinates to other Lie-groups and higher dimensional manifolds.

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Computing and Understanding Representation Varieties Efficiently | curve.unhyperbolic.org Reviews

https://curve.unhyperbolic.org

Identify the representations that correspond to geometric structures. A PGL(2,C)-representation corresponds to a hyperbolic structure if all shapes have positive imaginary part. There should be a similar condition for spherical CR-structures and real flag structures. Understand the mysterious duality between the shape and Ptolemy coordinates. Generalize the shape and Ptolemy coordinates to other Lie-groups and higher dimensional manifolds.

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curve.unhyperbolic.org

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Computing and Understanding Representation Varieties Efficiently

http://www.curve.unhyperbolic.org/people.html

Institut de Mathématiques de Jussieu. Georgia Institute of Technology. Institut de Mathématiques de Jussieu. Institut de Mathématiques de Jussieu.

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Computing and Understanding Representation Varieties Efficiently

http://www.curve.unhyperbolic.org/software.html

Is part of the popular 3-manifold software SnapPy and can be used to find boundary-unipotent representations of a 3-manifold into PGL(N,C) and compute invariants such as volume and Chern-Simons invariant.

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Computing and Understanding Representation Varieties Efficiently

http://www.curve.unhyperbolic.org/database.html

Data for SnapPy manifolds. Our data contains the primary decompositions of the Ptolemy varieties as well as the volume of each representation (see notes and caveats. For more). The manifolds for which we have complete data include:. OrientableCuspedCensus: all manifolds up to 9 simplices. LinkExteriors: all manifolds up to 16 simplices. HTLinkExteriors: all manifolds up to 13 simplices but L14n31302. OrientableCuspedCensus: all manifolds up to 3 simplices and selected manifolds with 4.

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Computing and Understanding Representation Varieties Efficiently

http://www.curve.unhyperbolic.org/activities.html

August 7-11, 2017. University of Maryland, College Park. June 22-26, 2015. Institute de Mathématique de Jussieu. REU project: 3-manifolds, triangulations, and volume computations. July 9 - August 1, 2014. And involves two students: Stephen Gilles (Maryland) and Peter Huston (Otterbein). A project description can be found here. And data can be found here.

5

Computing and Understanding Representation Varieties Efficiently

http://www.curve.unhyperbolic.org/results.html

Duality and invariants of representations of fundamental groups of 3-manifolds into PGL(3,C). E Falbel, Qingxue Wang. We determine the explicit transformation under duality of generic configurations of four flags in PGL(3,C) in cross-ratio coordinates. As an application we prove the invariance under duality of an invariant in the Bloch group obtained from decorated triangulations of 3-manifolds. Fock-Goncharov coordinates for rank two Lie groups. Christian K. Zickert. Christian K. Zickert. This paper pro...

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ptolemy.unhyperbolic.org

Data for SnapPy manifolds

http://ptolemy.unhyperbolic.org/html/summary.html

Data for SnapPy manifolds. Up to 8 tetrahedra. All but 11 2, 11 148, 11 357, 11 367, 11 369. M022, m023, m026, m027, m029, m030, m032, m033, m034, m035, m036, m037, m038, m043, m044, m045, m046, m052, m053, m054, m055, m060, m069, m070, m081, m082, m100, m117, m125, m129, m130, m135, m136, m137, m142, m146, m148, m149, m202, m203. Explanations (also see notes and caveats. Name of manifold in SnapPy census. We use the SnapPy triangulation. A checkmark indicates that a representation is induced from a repr...

sgt.imj-prg.fr

CURVE Conference 2017 » CURVE Conference 2017

http://sgt.imj-prg.fr/www/curve2017

The Conference CURVE 2017 takes place August 7-11 at University of Maryland, College Park. Martin Deraux, Antonin Guilloux. And the Graphene Theme.

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Conference web site » SGT

http://sgt.imj-prg.fr/www/blog/2015/01/19/hello-world

Geometric Structures and Triangulations. The web site of the conference CURVE 2017 is now open. Please visit. Http:/ sgt.imj-prg.fr/www/curve2017. This post has no tag. Analyse Algébrique team (IMJ-PRG). Analyse Complexe et Géométrie team (IMJ-PRG). ANR - SGT Project. And the Graphene Theme.

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CURVE Conference » CURVE'2015

http://sgt.imj-prg.fr/www/curve2015

The Conference CURVE 2015 is located at University Paris 6 (UPMC), bâtiment Esclangon. From June 22nd to June 25th. Martin Deraux, Antonin Guilloux. And the Graphene Theme.

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curve.unhyperbolic.org

Computing and Understanding Representation Varieties Efficiently

Identify the representations that correspond to geometric structures. A PGL(2,C)-representation corresponds to a hyperbolic structure if all shapes have positive imaginary part. There should be a similar condition for spherical CR-structures and real flag structures. Understand the mysterious duality between the shape and Ptolemy coordinates. Generalize the shape and Ptolemy coordinates to other Lie-groups and higher dimensional manifolds.

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