Exotic smooth structures on 4-manifolds. II
The author continues his investigation of exotic smooth structures of smooth 4-manifolds studied in [Forum Math. 14, 915-929 (2002; Zbl 1009.57029)], in which he obtained results for the nonspin positive signature case. In [Math. Z. 240, 405-421 (2002; Zbl 1030.57032)] he also studied the spin case. In the paper under review he studies the remaining case of nonspin smooth 4-manifolds with positive signature. His main result is: There is an increasing sequence \(\{m_i\}\) with \(m_i \to 9\) such that every simply connected, closed, nonspin, irreducible, smooth 4-manifold satisfying \(0 \leq {\mathbf c} \leq m_i\chi\) and \(b_i^+ \geq C_i\) odd (\(C_i\) is a constant depending on \(m_i\)) admits infinitely many, both symplectic and non-symplectic, exotic smooth structures. The primary techniques used are again fiber sum, logarithmic transform and Fintushel-Stern knot surgery [\textit{R. Fintushel} and \textit{R. J. Stern}, Invent. Math. 134, 363-400 (1998; Zbl 0914.57015)]. The main new ingredient is a technique due to \textit{A. Stipsicz} [Turk. J. Math. 23, 145-150 (1999; Zbl 0945.57010)].
scientific article; zbMATH DE number 1974772