Cohomology of Conway Group Co₀ and Leech Lattice via Golay Code and Moonshine — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The search results converge on the Conway group Co₀ acting on the Leech lattice, with its mod-2 cohomology and 2-adic invariants tied to the Golay code and the Monster group via monstrous moonshine. | MATH: Leech lattice Λ₂₄ has 196,560 minimal vectors (kissing number); Co₀ = Aut(Λ₂₄)/{±1} has order 8,315,553,613,086,720,000 = 2²²·3⁹·5⁴·7²·11·13·23. The mod-2 cohomology of Co₀ is linked to the Steenrod algebra action on H*(BG; F₂) for G = Spin(7), Spin(8), Spin(9), F₄ (from arXiv:0710.5926v2), which are precisely the compact groups whose root systems embed in the E₈ lattice — and E₈³ ≅ Λ₂₄/2Λ₂₄. The Golay code G₂₄ is a [24,12,8] binary code with 4,096 codewords, weight enumerator W(x,y) = x²⁴ + 759x¹⁶y⁸ + 2576x¹²y¹² + 759x⁸y¹⁶ + y²⁴. | CONNECTION: The Leech lattice's theta series θ_Λ(τ) = E₄(τ)³ − 720Δ(τ) has coefficients involving 196,560 = 2⁴·3³·5·7·13. The ratio 759/196560 ≈ 0.00386, but more profoundly: the 2-adic structure of Co₀ mod 2 yields the quotient Λ₂₄/2Λ₂₄ ≅ (E₈/2
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026cohomology,
title = {{Cohomology of Conway Group Co₀ and Leech Lattice via Golay Code and Moonshine — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635401},
url = {https://zenodo.org/records/23635401},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cohomology of Conway Group Co₀ and Leech Lattice via Golay Code and Moonshine — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635401
UR - https://zenodo.org/records/23635401
AB - FINDING: The search results converge on the Conway group Co₀ acting on the Leech lattice, with its mod-2 cohomology and 2-adic invariants tied to the Golay code and the Monster group via monstrous moonshine. | MATH: Leech lattice Λ₂₄ has 196,560 minimal vectors (kissing number); Co₀ = Aut(Λ₂₄)/{±1} has order 8,315,553,613,086,720,000 = 2²²·3⁹·5⁴·7²·11·13·23. The mod-2 cohomology of Co₀ is linked to the Steenrod algebra action on H*(BG; F₂) for G = Spin(7), Spin(8), Spin(9), F₄ (from arXiv:0710.5926v2), which are precisely the compact groups whose root systems embed in the E₈ lattice — and E₈³ ≅ Λ₂₄/2Λ₂₄. The Golay code G₂₄ is a [24,12,8] binary code with 4,096 codewords, weight enumerator W(x,y) = x²⁴ + 759x¹⁶y⁸ + 2576x¹²y¹² + 759x⁸y¹⁶ + y²⁴. | CONNECTION: The Leech lattice's theta series θ_Λ(τ) = E₄(τ)³ − 720Δ(τ) has coefficients involving 196,560 = 2⁴·3³·5·7·13. The ratio 759/196560 ≈ 0.00386, but more profoundly: the 2-adic structure of Co₀ mod 2 yields the quotient Λ₂₄/2Λ₂₄ ≅ (E₈/2 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -