Pinwheels and nullhomologous surgery on 4-manifolds with b^+ = 1

Abstract

We present a method for finding embedded nullhomologous tori in standard 4-manifolds which can be utilized to change their smooth structure. As an application, we show how to obtain infinite families of simply connected smooth 4-manifolds with b^+ = 1 and b^- = 2,...,7, via surgery on nullhomologous tori embedded in the standard manifolds CP^2 # k (-CP^2), k=2,...,7.

Final version. To appear in AGT

References in corpus (5)

• Exotic smooth structures on 4-manifolds with zero signature
• Exotic Smooth Structures on Small 4-Manifolds
• Surgery on Nullhomologous Tori
• A symplectic manifold homeomorphic but not diffeomorphic to CP^2 # 3(-CP^2)
• Surgery on nullhomologous tori and simply connected 4-manifolds with b^+=1

Cited by in corpus (8)

• Surgery along star shaped plumbings and exotic smooth structures on 4-manifolds
• New Homotopy 4-Spheres
• Topologically isotopic and smoothly inequivalent 2-spheres in simply connected 4-manifolds whose complement has a prescribed fundamental group
• Small Lefschetz Fibrations on Simply-Connected $4$-Manifolds
• Smoothly knotted and topologically unknotted nullhomologous surfaces in 4-manifolds
• An adjunction criterion in almost-complex 4-manifolds
• On fillings of homotopy equivalent contact structures
• On Nash's 4-sphere and Property 2R