On the geography of simply connected nonspin symplectic 4-manifolds with nonnegative signature

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• 作者：Anar Akhmedov ; ^{akhmedov@math.umn.edu" class="auth_mail" title="E-mail the corresponding author} ; Sü ; meyra Sakallı ^{sakal008@math.umn.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 57R55 ; secondary ; 57R57 ; 57M05
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：15 June 2016
• 年：2016
• 卷：206
• 期：Complete
• 页码：24-45
• 全文大小：666 K

文摘

In  and , the first author and his collaborators constructed the irreducible symplectic 4-manifolds that are homeomorphic but not diffeomorphic to 74&_mathId=si1.gif&_user=111111111&_pii=S0166864116300074&_rdoc=1&_issn=01668641&md5=5ac813a056ffc0739408cae062643a87">74-si1.gif">$(2n-1){\mathbb{CP}}^2\mathrm{\#}(2n-1){\overline{\mathbb{CP}}}^2$ for each integer 74&_mathId=si2.gif&_user=111111111&_pii=S0166864116300074&_rdoc=1&_issn=01668641&md5=0bbd6e24681fa828309375d0e06211c3" title="Click to view the MathML source">n≥25$n\ge \mathrm{<font\; color="red">25</font>}$, and the families of simply connected irreducible nonspin symplectic 4-manifolds with positive signature that are interesting with respect to the symplectic geography problem. In this paper, we improve the main results in  and . In particular, we construct (i) an infinitely many irreducible symplectic and nonsymplectic 4-manifolds that are homeomorphic but not diffeomorphic to 74&_mathId=si1.gif&_user=111111111&_pii=S0166864116300074&_rdoc=1&_issn=01668641&md5=5ac813a056ffc0739408cae062643a87">74-si1.gif">$(2n-1){\mathbb{CP}}^2\mathrm{\#}(2n-1){\overline{\mathbb{CP}}}^2$ for each integer 74&_mathId=si22.gif&_user=111111111&_pii=S0166864116300074&_rdoc=1&_issn=01668641&md5=2bb034860e695ccb5e2913cf5269af48" title="Click to view the MathML source">n≥12$n\ge 12$, and (ii) the families of simply connected irreducible nonspin symplectic 4-manifolds that have the smallest Euler characteristics among the all known simply connected 4-manifolds with positive signature and with more than one smooth structure. Our construction uses the complex surfaces of Hirzebruch and Bauer–Catanese on Bogomolov–Miyaoka–Yau line with 74&_mathId=si17.gif&_user=111111111&_pii=S0166864116300074&_rdoc=1&_issn=01668641&md5=bc91a13981fd3a0dc7b43776bfd6b9d4">74-si17.gif">$c_1^2=9{\chi }_h=45$, along with the exotic symplectic 4-manifolds constructed in , , ,  and .