PreprintCC BY 4.0arXiv
Irreducible exotic ℂℙ2# 7ℂ̅ ℙ 2's with free involutions
Abstract
We construct infinitely many pairwise non-diffeomorphic irreducible smooth four-manifolds homeomorphic to ℂℙ2# 7ℂ̅ ℙ 2, each admitting a free, orientation-preserving involution. Their quotients give infinitely many irreducible definite four-manifolds with fundamental group ℤ/2 ℤ and b2=3, filling the corresponding gap in the geography of such examples. The construction of infinitely many distinct examples relies on a novel equivariant torus surgery.
Related
- Exotic involutions on irreducible 4-manifolds from Real Seiberg--Witten theory
- Structure of irreducible homomorphisms to/from free and injective modules
- Quivers with Involutions and Shifted Twisted Yangians via Coulomb Branches
- Some Coble surfaces admit only Bertini involutions
- Sylow $2$-Subgroups of Finite Groups with a Single Conjugacy Class of Involutions
BibTeX
@misc{baykur2026irreducible,
title = {{Irreducible exotic $\mathbb CP^2\# 7\overline \mathbb C \mathbb P ^2$'s with free involutions}},
author = {R. İnanç Baykur and András I. Stipsicz and Zoltán Szabó},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26450},
eprint = {2609.26450},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26450},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Irreducible exotic ℂℙ^2# 7ℂ̅ ℙ ^2's with free involutions
AU - R. İnanç Baykur
AU - András I. Stipsicz
AU - Zoltán Szabó
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26450
UR - https://arxiv.org/abs/2609.26450
AB - We construct infinitely many pairwise non-diffeomorphic irreducible smooth four-manifolds homeomorphic to ℂℙ^2# 7ℂ̅ ℙ ^2, each admitting a free, orientation-preserving involution. Their quotients give infinitely many irreducible definite four-manifolds with fundamental group ℤ/2 ℤ and b_2=3, filling the corresponding gap in the geography of such examples. The construction of infinitely many distinct examples relies on a novel equivariant torus surgery.
ER -