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Self-Conjugate Vectors of Immersed Manifolds in R6
Daniel Dreibelbis University of North Florida USA
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Shameless Self-promotion
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Outline Define conjugate and self-conjugate vectors, focusing on the case of 3-manifolds in Euclidean 6-space. Look at connection between conjugate vectors and elliptic curves. Classify generic structure of the parabolic set. Classify generic transitions in a 1-parameter family of parabolic sets.
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Conjugate Vectors
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Special Case
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Description of Conjugate Vectors
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Curvature Veronese Surface
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Possible Configurations
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Elliptic Curves - Addition
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Conjugate Map The conjugate map is the sum of an order 2 point:
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Almost Normal Form
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Classification Same curve can have different conjugate maps, one for each point of order 2. j-invariant and conjugate map determines affine type of conjugate curve
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Self-Conjugate Vectors
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Page 1
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Page 167
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Parabolic Set
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Generic Structure of the Parabolic Set
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Around a Triple Point
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Through a Pinch Point
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Generic Changes
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A3 vectors and Morse Transitions
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A3 vectors and Morse Transitions
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Quadruple Point
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Pinch Point Intersection
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