Exotic diffeomorphisms of 4-manifolds with b_+ = 2

David Baraglia; Joshua Tomlin

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arXiv · 2511.13976

Exotic diffeomorphisms of 4-manifolds with b_+ = 2

David Baraglia·Joshua Tomlin

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Abstract

Let $X$ be a compact, oriented, smooth, simply-connected $4$-manifold. The mapping class group of $X$ is defined as the group of smooth isotopy classes of diffeomorphisms of $X$. The Torelli group of $X$ is the subgroup of the mapping class group consisting of smooth isotopy classes of diffeomorphisms which are continuously isotopic to the identity. We prove that for each $n \ge 10$, the Torelli group of $2\mathbb{CP}^2 \# n \overline{\mathbb{CP}^2}$ surjects to $\mathbb{Z}^\infty$. We also prove that the mapping class group of $2 \mathbb{CP}^2 \# 10 \overline{\mathbb{CP}^2}$ is not finitely generated. Our proofs of these results makes use of Seiberg-Witten invariants for $1$-parameter familes of $4$-manifolds and in particular a gluing formula for connected sum families. Since the manifolds we consider have $b_+ = 2$, the chamber structure of the $1$-parameter Seiberg-Witten invariants plays an important role.

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BibTeX RIS

David Baraglia, Joshua Tomlin. 2025-11-17. Exotic diffeomorphisms of 4-manifolds with b_+ = 2. https://arxiv.org/abs/2511.13976

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