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Diff — Genus (mathematics)

Revision #1260 → #2102 · back to history

modifiedGenus (intuitive notion)c8f49cb829e7
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noteNo topological notion of genus (number of handles) is defined anywhere in Mathlib.No topological notion of genus (number of handles) is defined anywhere in Mathlib (grep for 'genus' in Mathlib returns no files).
addedGenus–Euler-characteristic relation for closed surfaces74a6f7c8c107
modifiedNon-orientable genus66c68de063ec
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noteNon-orientable genus and cross-caps are not formalized in Mathlib (a grep for crossCap/Klein bottle finds only the KleinFour group).Non-orientable genus and cross-caps are not formalized in Mathlib (grep for crossCap and Klein bottle finds nothing topological).
addedNon-orientable genus–Euler-characteristic relation2266f84de3d6
modifiedNon-orientable genus of projective plane and Klein bottle454105842a98
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noteMathlib has no projective-plane or Klein-bottle surface with an associated genus.Mathlib's only ProjectivePlane is the combinatorial incidence-geometry one (Mathlib.Combinatorics.Configuration), with no Klein-bottle surface or genus.
modifiedGenus of a knotdca586227972
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noteMathlib contains no knot theory, Seifert surfaces, or knot genus.Mathlib contains no knot theory, Seifert surfaces, or knot genus (grep for Seifert finds nothing).
modifiedGenus of a handlebodydfefa8d075ec
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noteHandlebodies and their genus are absent from Mathlib.Handlebodies and their genus are absent from Mathlib (grep for handlebody finds nothing).
modifiedElliptic curve as genus 1 curvee30a2fdac04f
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noteMathlib formalizes elliptic curves as Weierstrass curves with invertible discriminant (WeierstrassCurve.IsElliptic), not via the genus-1-with-rational-point characterization.Mathlib formalizes elliptic curves as Weierstrass curves with invertible discriminant (WeierstrassCurve.IsElliptic, confirmed), not via the genus-1-with-rational-point characterization.
modifiedGenus formula via Riemann–Roch72c066e9e266
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noteMathlib has no Riemann–Roch theorem for curves and no degree-genus formula.Mathlib has no Riemann–Roch theorem for curves and no degree-genus formula (grep for RiemannRoch finds nothing).
modifiedGenus of an oriented manifold (cobordism)54b0fb838565
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noteCobordism and genera in the sense of cobordism invariants are not present in Mathlib.Cobordism and genera in the sense of cobordism invariants are not present in Mathlib (the only 'cobord' matches are 'coborder' of immersions).
modifiedEuler characteristic is not a genus17ee0df37990
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noteMathlib has an algebraic Euler characteristic (HomologicalComplex.eulerChar) but no cobordism framework in which to state that it fails to be a genus.Mathlib has an algebraic Euler characteristic (in Mathlib.Algebra.Homology.EulerCharacteristic) but no cobordism framework in which to state that it fails to be a genus.