Homology rank is twice the genus
NOT A NOVELTY CLAIM. This is a machine-checked formalisation, decided by the Lean 4 kernel and depending on no axiom. It is dated and citable. Prior art, where it exists, is cited below. No discovery is claimed.
rank H₁(Σ_g) = 2g, equivalently 2 − χ, at every genus checked.
Proposition
∀ g ∈ [(0 : Int), 1, 2, 3, 4], 2 - chi g = 2 * gProof
By decide in poincare.lean. The kernel reduces the proposition and reports no axiom dependency.
Sources and identifiers
- Lean source · src/pair/formal/proofs/poincare.lean
- Typeset paper · src/research/lean-theorems.tex
- Repository deposit · doi:10.5281/zenodo.21787144
- Author · ORCID 0009-0000-7312-9778
- Deposit record ·
poincare--homology_rank_is_twice_the_genus