New exotic 4-manifolds via Luttinger surgery on Lefschetz fibrations

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dc.contributor.authorAkhmedov, Anaren
dc.contributor.authorSaglam, Kadriye Nuren
dc.contributor.departmentMathematicsen
dc.date.accessioned2021-01-05T06:57:54Zen
dc.date.available2021-01-05T06:57:54Zen
dc.date.issued2015-01-01en
dc.date.updated2021-01-05T06:57:51Zen
dc.description.abstractIn [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.en
dc.description.notes21 pages, 7 figures. One reference added, a few extra clarifying comments addeden
dc.description.versionPublished (Publication status)en
dc.format.extent21 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1142/S0129167X1550010Xen
dc.identifier.eissn1793-6519en
dc.identifier.issn0129-167Xen
dc.identifier.issue1en
dc.identifier.urihttp://hdl.handle.net/10919/101733en
dc.identifier.volume26en
dc.language.isoenen
dc.publisherWorld Scientificen
dc.rightsIn Copyright (InC)en
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectMathematicsen
dc.subject4-manifoldsen
dc.subjectexotic smooth structuresen
dc.subjectsymplectic 4-manifoldsen
dc.subjectLefschetz fibrationen
dc.subjectsymplectic sumen
dc.subjectLuttinger surgeryen
dc.subjectSMOOTH STRUCTURESen
dc.subjectLAGRANGIAN TORIen
dc.subjectSIGNATUREen
dc.subjectmath.GTen
dc.subjectmath.AGen
dc.subjectmath.SGen
dc.subject0101 Pure Mathematicsen
dc.subjectGeneral Mathematicsen
dc.titleNew exotic 4-manifolds via Luttinger surgery on Lefschetz fibrationsen
dc.title.serialInternational Journal of Mathematicsen
dc.typeArticle - Refereeden
dc.type.otherArticleen
dc.type.otherJournalen
pubs.organisational-group/Virginia Tech/Scienceen
pubs.organisational-group/Virginia Tech/Science/Mathematicsen
pubs.organisational-group/Virginia Techen

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