Akhmedov, AnarSaglam, Kadriye Nur2021-01-052021-01-052015-01-010129-167Xhttp://hdl.handle.net/10919/101733In [Small exotic 4-manifolds, Algebr. Geom. Topol. 8 (2008) 1781-1794], the first author constructed the first known example of exotic minimal symplectic CP2#5CP2and minimal symplectic 4-manifold that is homeomorphic but not diffeomorphic to 3CP2#7CP2. The construction in [Small exotic 4-manifolds, Algebr. Geom. Topol. 8 (2008) 1781-1794] uses Yukio Matsumoto's genus two Lefschetz fibrations on T2×S2#4CP 2 over S2along with the fake symplectic S2×S2construction given in [Construction of symplectic cohomology S2×S2, Proc. Gökova Geom. Topol. Conf. 14 (2007) 36-48]. The main goal in this paper is to generalize the construction in [Small exotic 4-manifolds, Algebr. Geom. Topol. 8 (2008) 1781-1794] using the higher genus versions of Matsumoto's fibration constructed by Mustafa Korkmaz and Yusuf Gurtas on σk × S2#4nCP 2 for any k ≥ 2 and n = 1, and k ≥ 1 and n ≥ 2, respectively. Using our symplectic building blocks, we also construct new symplectic 4-manifolds with the free group of rank s ≥ 1, the free product of the finite cyclic groups, and various other finitely generated groups as the fundamental group.21 page(s)application/pdfenIn Copyright (InC)Mathematics4-manifoldsexotic smooth structuressymplectic 4-manifoldsLefschetz fibrationsymplectic sumLuttinger surgerySMOOTH STRUCTURESLAGRANGIAN TORISIGNATUREmath.GTmath.AGmath.SG0101 Pure MathematicsGeneral MathematicsArticle - Refereed2021-01-05https://doi.org/10.1142/S0129167X1550010X2611793-6519