Exotic non-orientable four-manifolds with prescribed fundamental group

Key Points

• The central aim is to determine how finitely presented groups can serve as fundamental groups for certain non-orientable four-manifolds.
• Constructed non-orientable four-manifolds with specific fundamental groups using a Gluck twist.
• Analyzed orientation 2-covers for diffeomorphism properties.
• Investigated the stability of smooth structures with regards to added manifold components.
• Each finitely presented group with an index two subgroup is realized as a fundamental group of a four-manifold.
• The orientation 2-covers of the constructed four-manifolds are diffeomorphic.
• The two smooth structures remain inequivalent even after adding multiple copies of the product of 2-spheres.