Exotic $$G_2$$-manifolds

Exotic aspherical manifolds

Small Exotic 4-manifolds

In this article, we construct the first examples of a simply connected minimal symplectic 4-manifold homeomorphic but not diffeomorphic to 3CP #7CP 2 . We also construct the first exotic symplectic structure on CP #5CP 2 .

Exotic Smooth Structures on Small 4-manifolds

Let M be either CP#3CP or 3CP#5CP. We construct the first example of a simply-connected symplectic 4-manifold that is homeomorphic but not diffeomorphic to M .

Exotic Structures on Smooth 4-manifolds

A short survey of exotic smooth structutes on 4-manifolds is given with a special emphasis on the corresponding cork structures. Along the way we discuss some of the more recent results in this direction, obtained jointly with R. Matveyev, B.Ozbagci, C.Karakurt and K.Yasui.

On Park’s Exotic Smooth Four-manifolds

In a recent paper, Park constructs certain exotic simply-connected fourmanifolds with small Euler characteristics. Our aim here is to prove that the fourmanifolds in his constructions are minimal.