Exotic smooth structures on 4-manifolds. II
type: Item
instance of: scholarly article
title: Exotic smooth structures on 4-manifolds. II
zbMATH Open document ID: 1028.57032
DOI: 10.1016/S0166-8641(03)00033-6
published in: Topology and its Applications
publication date: 2003-09-04T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 57R57
Mathematics Subject Classification ID: 57R17
Mathematics Subject Classification ID: 57R55
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 1974772
zbMATH Keywords: exotic smooth structure
zbMATH Keywords: fiber sum
zbMATH Keywords: irreducible
zbMATH Keywords: nonspin
author: Jongil Park
reviewed by: Terry Lawson
MaRDI profile type: Publication
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full work available at URL: s0166-8641(03)00033-6
OpenAlex ID: W1980861110
description: scientific article; zbMATH DE number 1974772