In low-dimensional topology, a branch of mathematics, the E8 manifold is the unique compact, simply connected topological 4-manifold with intersection form the E8 lattice.
manifold was discovered by Michael Freedman in 1982.
Rokhlin's theorem shows that it has no smooth structure (as does Donaldson's theorem), and in fact, combined with the work of Andrew Casson on the Casson invariant, this shows that the
The manifold can be constructed by first plumbing together disc bundles of Euler number 2 over the sphere, according to the Dynkin diagram for
, a 4-manifold whose boundary is homeomorphic to the Poincaré homology sphere.