In mathematics, the E₈ manifold is the unique compact, simply connected topological 4-manifold with intersection form the E₈ lattice.

This article provides insufficient context for those unfamiliar with the subject. (July 2021)

The ${\displaystyle E_{8}}$ 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 ${\displaystyle E_{8}}$ manifold is not even triangulable as a simplicial complex.

The manifold can be constructed by first plumbing together disc bundles of Euler number 2 over the sphere, according to the Dynkin diagram for ${\displaystyle E_{8}}$. This results in ${\displaystyle P_{E_{8}}}$, a 4-manifold whose boundary is homeomorphic to the Poincaré homology sphere. Freedman's theorem on fake 4-balls then says we can cap off this homology sphere with a fake 4-ball to obtain the ${\displaystyle E_{8}}$ manifold.

• E₈ (mathematics) – 248-dimensional exceptional simple Lie group
• Glossary of topology – Mathematics glossary
• List of geometric topology topics