Documentation

LeanPool.JacobianDiffgeo.SphereTopology

sphere-topology: SimplyConnectedSpace (OnePoint ℂ) and genus X = 0 for simply connected X #

API summary (see docs/design/sphere-topology.md), namespace RS.SphereTopology unless noted. Builds on projective-line (CC5) and paths-and-integrals (CC6); no van Kampen, no universal cover, no covering-space monodromy anywhere — the two headline results are assembled from more elementary mathlib pieces (contractibility/local-path-connectedness/open-embedding transport) plus paths-and-integrals' own loop-perturbation and homotopy-invariance lemmas.

Downstream consumers: genus-zero-headline (consumes genus_eq_zero_of_homeo_sphere directly); monodromy (may reuse contMDiff_and_mdifferential_eq_of_isPrimitiveAlongMap_id verbatim, or re-derive the same conclusion from its own chain-continuation IsPrimitiveAlongMap id η F univ fact — both routes agree, no dependency is required either way).