Alphabeta MathCoupled Penrose vanishing on the round four-sphere
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1 · Prerequisites
Abstract Algebra
- Algebraic Closure, Embeddings, and Separability
- Algebraic Extensions, Extension Degree, and Finite Fields
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- Composition Series, the Jordan–Hölder Theorem and Solvable Groups
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Algebraic Geometry
Algebraic Topology
Category Theory
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Complex Analysis
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Differential Geometry
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Functional Analysis
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Linear Algebra
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Measure Theory
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Number Theory
Partial Differential Equations
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Quantum Field Theory Mathematics
Real Analysis
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- pi: the Equivalent Characterizations
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- The Cantor Set, Baire Category, and Measure Zero in ℝ
- The Complex Exponential and Euler's Formula
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- The Fundamental Theorems of Calculus
- The Inverse and Implicit Function Theorems
- The Inverse Function Theorem Completed
- The Logarithm and General Powers
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- Topology of ℝ
Scheme Theory
Set Theory
- Cardinal Arithmetic, Cofinality and the Alephs
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Topology
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- Metric Spaces
- Partitions of Unity and Paracompactness
- Separation Axioms: the Hierarchy
- Subspaces, Products, and Quotients
- The Topology of Euclidean Space
- Topological Spaces and Continuity
2 · Logical flowchart
3 · Items
Definition
Positive incidence geometry for the coupled Penrose transform
Lemma
Incidence alpha planes detect positive-orientation anti-self-duality
Lemma
Scalar curvature of the unit round four-sphere
Lemma
Dolbeault groups of the negative twistor-fibre twists
Lemma
Injective fibre-harmonic edge for coupled Penrose cohomology
Lemma
Round coupled Penrose correction gives the R-over-six operator
Theorem