Computing and Understanding Representation Varieties Efficiently

Identify the representations that correspond to geometric structures. A PGL2,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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Unhyperbolic

Module is part of the popular 3-manifold software SnapPy. The Ptolemy varities can be computed using Magma. Or retrieved automatically from our precomputed database.

SGT Geometric Structures and Triangulations

The web site of the conference CURVE 2017 is now open. The true starting point of the CURVE project was the conference.

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TITLE

Computing and Understanding Representation Varieties Efficiently

DESCRIPTION

Identify the representations that correspond to geometric structures. A PGL2,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.

CONTENT

This web site states the following, "Identify the representations that correspond to geometric structures." Our analyzers saw that the web site stated " A PGL2,C-representation corresponds to a hyperbolic structure if all shapes have positive imaginary part." The Website also said " 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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