Some examples of small irreducible exotic 4-manifolds with free abelian fundamental group

Valentina Bais; Rafael Torres; Daniele Zuddas

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arXiv · 2410.06642

Some examples of small irreducible exotic 4-manifolds with free abelian fundamental group

Valentina Bais·Rafael Torres·Daniele Zuddas

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Abstract

We produce examples of pairwise non-diffeomorphic closed irreducible 4-manifolds with non-trivial free abelian fundamental group of rank less than three and small Euler characteristic. These exotic smooth structures become standard after taking a connected sum with a single copy of $S^2\times S^2$. The contributions of this paper include an explicit mechanism to computate the equivariant intersection form of 4-manifolds that are obtained via torus surgeries and a new stabilization result concerning exotic smooth structures with arbitrary fundamental group.

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Valentina Bais, Rafael Torres, Daniele Zuddas. 2024-10-09. Some examples of small irreducible exotic 4-manifolds with free abelian fundamental group. https://arxiv.org/abs/2410.06642

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