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Computing the image of Thurston’s skinning map
David Dumas Richard Kent
University of Illinois at Chicago University of Wisconsin – Madison
September 17, 2013
Computing the image of Thurstons skinning map David Dumas Richard - - PowerPoint PPT Presentation
Computing the image of Thurstons skinning map David Dumas Richard - - PowerPoint PPT Presentation
Computing the image of Thurstons skinning map David Dumas Richard Kent University of Illinois at Chicago University of Wisconsin Madison September 17, 2013 The Skinning Map Goal: Compute and see image of M The Examples The Method
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The Examples
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The Method
Intersections in the character variety
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The Implementation
Triangulate the fiber product
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The Flayer
Demonstration of fiber product reconstruction
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Gallery of skinning map images
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Oct1 – Rectangular boundary [cf. Chesebro-Deblois]
[−2, 2] × [0, 4]
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Oct1 – Rectangular boundary [cf. Chesebro-Deblois]
[−2, 2] × [0, 4]
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Oct1 – Rectangular boundary [cf. Chesebro-Deblois]
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Oct1 – Rectangular boundary [cf. Chesebro-Deblois]
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Oct2 – Tetrahedral boundary [cf. Gaster]
[−2, 2] × [0, 4]
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Oct2 – Tetrahedral boundary [cf. Gaster]
[−2, 2] × [0, 4]
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Oct2 – Tetrahedral boundary [cf. Gaster]
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Oct2 – Tetrahedral boundary [cf. Gaster]
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Oct3 – Square boundary
[−2, 2] × [0, 4]
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Oct3 – Square boundary
[−2, 2] × [0, 4]
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Oct3 – Square boundary
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Oct3 – Square boundary
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Oct3 – Square boundary
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The Octahedral Manifolds
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Tools
◮ Python! ◮ Flayer
◮ Fiber product 2-complex construction ◮ Rasterizer ◮ Fricke calculus and extension variety code generation ◮ Under development, source will be released
◮ cp1
◮ New library for CP1 structures ◮ Python ( + C + Cython + GSL) ◮ http://github.com/daviddumas/cp1