The $E_8$ manifold can be constructed by plumbing together disk bundles of Euler number $2$ over $2$-sphere $S^2$ according to the Dynkin diagram for $E_8$.

In question, it can be written that $E_8$ manifold cannot be smoothed by Donaldson's diagonalization theorem. Due to Freedman, on the other hand, $E_8$ manifold bounds a contractible topological $4$-manifold. So this is a very interesting example for $4$-dimensional topology.

Saveliev (as well as several mathematicians) wrote in this book Invariants of Homology 3-Spheres that such a plumbing construction gives rise to a simply connected smooth $4$-manifold.

Where is the problem? Are they just typos or pasting disk bundles create "corners" which cannot be smoothed so that the resulting $4$-manifold might not be smooth?

The $E_8$ manifold can be constructed by plumbing together disk bundles of Euler number $2$ over $2$-sphere $S^2$ according to the Dynkin diagram for $E_8$.

In Smooth 4-manifolds with $E_8$ intersection form, it is written that an $E_8$ manifold cannot be smoothed by Donaldson's diagonalization theorem. By Freedman - The topology of four-dimensional manifolds, on the other hand, $E_8$ manifold bounds a contractible topological $4$-manifold. So this is a very interesting example for $4$-dimensional topology.

Saveliev (as well as several mathematicians) wrote in the book Invariants of Homology 3-Spheres that such a plumbing construction gives rise to a simply connected smooth $4$-manifold.

Where is the problem? Are they just typos, or does pasting disk bundles create "corners" which cannot be smoothed so that the resulting $4$-manifold might not be smooth?