TY - JOUR
T1 - Definite four-manifolds with exotic smooth structures
AU - Stipsicz, András I.
AU - Szabó, Zoltán
N1 - Publisher Copyright:
© 2024 Walter de Gruyter GmbH, Berlin/Boston.
PY - 2024/12/1
Y1 - 2024/12/1
N2 - In this paper, we study smooth structures on closed, oriented four-manifolds with fundamental group Z/2Z and definite intersection form. We construct infinitely many irreducible, oriented, closed, definite, smooth four-manifolds with π1 = Z/2Z and b2 = 1, and b2 = 2. As an application, we prove that, when the second Betti number b2 of a definite four-manifold with π1 = Z/2Z is positive and it admits a smooth structure, then it admits infinitely many smooth structures.
AB - In this paper, we study smooth structures on closed, oriented four-manifolds with fundamental group Z/2Z and definite intersection form. We construct infinitely many irreducible, oriented, closed, definite, smooth four-manifolds with π1 = Z/2Z and b2 = 1, and b2 = 2. As an application, we prove that, when the second Betti number b2 of a definite four-manifold with π1 = Z/2Z is positive and it admits a smooth structure, then it admits infinitely many smooth structures.
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U2 - 10.1515/crelle-2024-0072
DO - 10.1515/crelle-2024-0072
M3 - Article
AN - SCOPUS:85207415357
SN - 0075-4102
VL - 2024
SP - 267
EP - 290
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 817
ER -