Cobordism, Moduli & Geometric Duality

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Abstractions about algebraic cobordism, dualities, external rays, flattening, and moduli stacks classifying formal group structures.

5 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Algebraic cobordism — Provide the universal oriented cohomology theory for smooth algebraic varieties, encoding projective pushforwards and first Chern classes through the universal one-dimensional commutative formal group law.
• Eckmann–Hilton Duality — Generate and test homotopy-theoretic counterpart concepts by expressing a construction categorically and reversing its arrows, with adjunctions and universal properties guiding—but never automatically validating—the transfer.
• External Ray — A constant-angle curve in an exterior conformal coordinate that approaches a Julia-set or connectedness-locus boundary from infinity and may land at a boundary point.
• Flattening — A dimensionless axial-compression measure for an ellipse or spheroid, ordinarily the semiaxis difference divided by the semimajor axis, with explicitly convertible alternative normalizations.
• Moduli Stack of Formal Group Laws — A coordinate-independent moduli stack obtained from formal group laws by quotienting coordinate changes, retaining isomorphisms and organizing formal groups by height for chromatic homotopy theory.