ptolemy.unhyperbolic.org

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Module 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. The Ptolemy varities can be computed using Magma. Or retrieved automatically from our precomputed database. 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. And Talk at ICERM.

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Unhyperbolic | ptolemy.unhyperbolic.org Reviews

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Module 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. The Ptolemy varities can be computed using Magma. Or retrieved automatically from our precomputed database. 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. And Talk at ICERM.

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1 about me

2 research

3 ptolemy

4 math links

5 old website

6 module

7 or sage

8 browsable database

9 individual magma files

10 tar archives

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Unhyperbolic | ptolemy.unhyperbolic.org Reviews

https://ptolemy.unhyperbolic.org

Module 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. The Ptolemy varities can be computed using Magma. Or retrieved automatically from our precomputed database. 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. And Talk at ICERM.

INTERNAL PAGES

ptolemy.unhyperbolic.org

1

ptolemy presentation at ICERM -- Sage

http://www.ptolemy.unhyperbolic.org/icermPresentation.html

Ptolemy presentation at ICERM. Demonstration of the ptolemy module. Be an orientable 3-manifold with boundary consisting of one or more tori given as ideal triangulation. If each peripheal subgroup is taken into a conjugate of. The subgroup of unit triangular matrices. Find all boundary-unipotent representations (up to conjugacy). And compute invariants such as (complex) volume, trace field, . Is hyperbolic, then the universal cover. The Decktransformations are in. And we get a boundary-unipotent. Vols =...

2

Data for SnapPy manifolds

http://www.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...

3

Index of /data/tar

http://www.ptolemy.unhyperbolic.org/data/tar

Data pgl2 HTLinkExteriors 12 to 13 tetrahedra.tar.bz2. 27-Jan-2014 21:53 95M data pgl2 HTLinkExteriors up to 11 tetrahedra.tar.bz2. 27-Jan-2014 21:52 6.5M data pgl2 LinkExteriors up to 16 tetrahedra.tar.bz2. 01-Oct-2013 01:50 18M data pgl2 OrientableCuspedCensus 08 tetrahedra.tar.bz2. 27-Jan-2014 21:52 601M data pgl2 OrientableCuspedCensus 09 tetrahedra.tar.bz2. 12-Oct-2014 02:50 6.6G data pgl2 OrientableCuspedCensus up to 07 tetrahedra.tar.bz2. 10-Sep-2013 11:14 31M data pgl3 and pgl4.tar.bz2.

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http://www.ptolemy.unhyperbolic.org/data

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Notes and caveats

http://www.ptolemy.unhyperbolic.org/notes.html

Notes and caveats (back to ptolemy. PGL(n,ℂ)-representations, obstruction classes and Ptolemy varieties. Each manifold in the SnapPy census is regarded as a manifold M with boundary a union of c tori, together with a topological ideal triangulation. For each boundary-unipotent representation ρ of π. M) in PGL(n,ℂ) there is an associated class in H. For each class σ in H. M,∂M; Z/nZ), the Ptolemy variety for σ is a variety P. Ptolemy coordinates and shapes. Together with the similar result (unpublished) i...

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unhyperbolic.org

Unhyperbolic

http://www.unhyperbolic.org/intro.html

Math and especially 3-dimensional geometry are most fascinating subjects. On this page, I am trying to give an introduction to the areas which fascinate me that is suitable for non-mathematicians as well. Of hyperbolic geometry in layman terms. Knot Not ( Part 1. Explaining why the complement of the Boromean rings is hyperbolic. Bill Thurson's Lecture The Mystery of 3-Manifolds. Bernd Sturmfels' Lecture on Gröbner Bases. Life of a mathematician: Shiing-Shen Chern. Armstrong and Miller's Physics Special.

unhyperbolic.org

Unhyperbolic

http://www.unhyperbolic.org/cv.html

Software Engineer at Pixar Animation Studios. June 2012 - ). PostDoc at University of Maryland. January 2012 - May 2012). Working with Christian Zickert. On representations of 3-manifold groups and software to compute them. Intern at Pixar Animation Studios. September 2011 - December 2011). UC Berkeley (December 2011). Title: Visualizing Regular Tessellations: Principal Congruence Links and Equivariant Morphisms from Surfaces to 3-Manifolds. Outside committee member: Carlo Sequin.

curve.unhyperbolic.org

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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Module 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. The Ptolemy varities can be computed using Magma. Or retrieved automatically from our precomputed database. 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. And Talk at ICERM.

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