Exotic smooth structures on 4-manifolds with zero signature

Abstract

For every integer $k\ge 2$, we construct infinite families of mutually nondiffeomorphic irreducible smooth structures on the topological $4$-manifolds $(2k-1)(S^2\times S^2)$ and $(2k-1)(\CP#\CPb)$, the connected sums of $2k-1$ copies of $S^2\times S^2$ and $\CP#\CPb$.

6 pages

References in corpus (5)

• An exotic smooth structure on CP^2+6CP^2-bar
• Reverse engineering small 4-manifolds
• Exotic Smooth Structures on Small 4-Manifolds
• Constructing infinitely many smooth structures on small 4-manifolds
• Kodaira dimension and symplectic sums

Cited by in corpus (10)

• Pinwheels and nullhomologous surgery on 4-manifolds with b^+ = 1
• Constructions of generalized complex structures in dimension four
• Surgery along star shaped plumbings and exotic smooth structures on 4-manifolds
• Genus two Lefschetz fibrations with $b_2^{+}=1$ and ${c_1}^2=1,2$
• Branched coverings of $C{P}^2$ and other basic 4-manifolds
• Deformation of Singular Fibers of Genus $2$ Fibrations and Small Exotic Symplectic $4$-Manifolds
• New Exotic 4-Manifolds via Luttinger Surgery on Lefschetz Fibrations
• Topologically isotopic and smoothly inequivalent 2-spheres in simply connected 4-manifolds whose complement has a prescribed fundamental group
• A cork of the rational surface with the second Betti number 9
• Kerler-Lyubashenko Functors on 4-Dimensional 2-Handlebodies