Exotic smooth structures on small 4-manifolds with odd signatures

Anar Akhmedov; B. Doug Park

doi:10.1007/s00222-010-0254-y

Exotic smooth structures on small 4-manifolds with odd signatures

Anar Akhmedov, B. Doug Park

Mathematics

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34 Scopus citations

Abstract

Let M be (2n - 1)ℂℙ²#2nℂℙ̄² for any integer n≥1. We construct an irreducible symplectic 4-manifold homeomorphic to M and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic 4-manifolds homeomorphic to M. We also construct such exotic smooth structures when M is ℂℙ²#4ℂℙ̄² or 3ℂℙ²#Kℂℙ̄² for k=6,8,10.

Original language	English (US)
Pages (from-to)	577-603
Number of pages	27
Journal	Inventiones Mathematicae
Volume	181
Issue number	3
DOIs	https://doi.org/10.1007/s00222-010-0254-y
State	Published - 2010

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title = "Exotic smooth structures on small 4-manifolds with odd signatures",

abstract = "Let M be (2n - 1)ℂℙ2#2nℂ{\=ℙ}2 for any integer n≥1. We construct an irreducible symplectic 4-manifold homeomorphic to M and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic 4-manifolds homeomorphic to M. We also construct such exotic smooth structures when M is ℂℙ2#4ℂ{\=ℙ}2 or 3ℂℙ2#Kℂ{\=ℙ}2 for k=6,8,10.",

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AB - Let M be (2n - 1)ℂℙ2#2nℂℙ̄2 for any integer n≥1. We construct an irreducible symplectic 4-manifold homeomorphic to M and also an infinite family of pairwise non-diffeomorphic irreducible non-symplectic 4-manifolds homeomorphic to M. We also construct such exotic smooth structures when M is ℂℙ2#4ℂℙ̄2 or 3ℂℙ2#Kℂℙ̄2 for k=6,8,10.

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Exotic smooth structures on small 4-manifolds with odd signatures

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