E8 manifold

Description

The $E_8$ manifold is the closed, simply connected, topological 4-manifold whose intersection form is the form of the $E_8$ lattice. This form is positive definite, even and unimodular, of rank $8$ and signature $8$. Its existence and its uniqueness up to homeomorphism follow from Freedman's classification, since the form is even. One construction plumbs together eight disk bundles over the $2$-sphere with Euler number $2$, following the pattern of the $E_8$ Dynkin diagram. The boundary of this plumbing is the Poincaré homology sphere. Freedman showed that this homology sphere bounds a contractible topological $4$-manifold, and gluing it to the plumbing along the common boundary gives the $E_8$ manifold.