Representing nonnegative homology classes of <IMG ALIGN=MIDDLE HEIGHT=34 WIDTH=105> by minimal genus smooth embeddings期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Representing nonnegative homology classes of by minimal genus smooth embeddings

Authors:	Bang-He Li

Institution:	Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, Peoples Republic of China

Abstract:	For any nonnegative class $\xi$ in $H_2({\mathbb C}P^2\#n{\overline{{\mathbb C}P}}{}^2, {\mathbf Z})$ , the minimal genus of smoothly embedded surfaces which represent $\xi$ is given for $n\leq 9$ , and in some cases with $n\geq 10$ , the minimal genus is also given. For the finiteness of orbits under diffeomorphisms with minimal genus , we prove that it is true for $n\leq 8$ with $g\geq 1$ and for $n\leq 9$ with $g\geq 2$ .

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