Exotic involutions on irreducible 4-manifolds from Real Seiberg--Witten theory

Abstract

Using Real Seiberg--Witten theory, Miyazawa constructed infinitely many exotic involutions on ℂℙ̅², and Baraglia extended this construction to X#ℂℙ̅² for a broad class of $4$-manifolds X equipped with an involution c. We show that, under suitable Real Seiberg--Witten hypotheses, the ℂℙ̅² summand can be omitted when X is non-spin and the complement of the fixed locus is simply-connected. Our construction also yields infinite families of topologically isotopic but smoothly non-isotopic embeddings of the branch surface in the quotient X/⟨ c⟩. As applications, we construct anti-holomorphic involutions on irreducible, simply-connected projective surfaces of general type with infinitely many exotic copies, none of which is anti-symplectic with respect to any orientation-compatible symplectic form. These surfaces include cyclic branched covers of ℂℙ² and complete intersections of multidegree (2,4k) in ℂℙ⁴.

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BibTeX RIS

BibTeX

@misc{jo2026exotic,
  title = {{Exotic involutions on irreducible 4-manifolds from Real Seiberg--Witten theory}},
  author = {Woohyeok Jo and Simone Tagliente},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40802},
  eprint = {2610.40802},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40802},
}

RIS

TY  - UNPB
TI  - Exotic involutions on irreducible 4-manifolds from Real Seiberg--Witten theory
AU  - Woohyeok Jo
AU  - Simone Tagliente
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40802
UR  - https://arxiv.org/abs/2610.40802
AB  - Using Real Seiberg--Witten theory, Miyazawa constructed infinitely many exotic involutions on ℂℙ̅^2, and Baraglia extended this construction to X#ℂℙ̅^2 for a broad class of $4$-manifolds X equipped with an involution c. We show that, under suitable Real Seiberg--Witten hypotheses, the ℂℙ̅^2 summand can be omitted when X is non-spin and the complement of the fixed locus is simply-connected. Our construction also yields infinite families of topologically isotopic but smoothly non-isotopic embeddings of the branch surface in the quotient X/⟨ c⟩. As applications, we construct anti-holomorphic involutions on irreducible, simply-connected projective surfaces of general type with infinitely many exotic copies, none of which is anti-symplectic with respect to any orientation-compatible symplectic form. These surfaces include cyclic branched covers of ℂℙ^2 and complete intersections of multidegree (2,4k) in ℂℙ^4.
ER  -

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