Exotic embedded surfaces and involutions from Real Seiberg-Witten theory
Date
2026
Authors
Baraglia, D.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
International Journal of Mathematics, 2026; 37(04):2650028-1-2650028-57
Statement of Responsibility
David Baraglia
Conference Name
Abstract
By using Real Seiberg–Witten theory, Miyazawa introduced an invariant of certain 4-manifolds with involution and used this invariant to construct infinitely many exotic involutions on CP2 and infinitely many exotic smooth embeddings of RP2 in S4. In this paper, we extend Miyazawa’s construction to a large class of 4-manifolds, giving many infinite families of involutions on 4-manifolds which are conjugate by homeomorphisms but not by diffeomorphisms and many infinite families of exotic embeddings of non-orientable surfaces in 4-manifolds, where exotic means continuously isotopic but not smoothly isotopic. Exoticness of our construction is detected using Real Seiberg–Witten theory. We study Miyazawa’s invariant, relate it to the Real Seiberg–Witten invariants of Tian–Wang and prove various fundamental results concerning the Real Seiberg–Witten invariants such as: relation to positive scalar curvature, wall-crossing, a mod 2 formula for spin structures, a localization formula relating ordinary and Real Seiberg–Witten invariants, a connected sum formula and a fiber sum formula.
School/Discipline
Dissertation Note
Provenance
Description
Access Status
Rights
© 2026 World Scientific Publishing Company.