In mathematics, a Barlow surface is one of the complex surfaces discovered by . They are simply connected surfaces of general type with pg=0. They are homeomorphic but not diffeomorphic to a projective plane blown up in 8 points. The Hodge diamond for the Barlow surfaces is:

Detection of exotic smooth structures

According to Freedman's classification, a simply connected oriented closed topological 4-manifold with intersection form. Any such smooth manifold with a non-vanishing Seiberg–Witten invariant with the induced smooth structure allows a Riemannian metric of positive scalar curvature (psc metric) and therefore has only vanishing Seiberg–Witten invariants.

See also

• Hodge theory

References