Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Representing nonnegative homology classes
of ${\mathbb C}P^2\#n{\overline{{\mathbb C}P}}{}^2$ by minimal genus smooth embeddings

Author: Bang-He Li
Journal: Trans. Amer. Math. Soc. 352 (2000), 4155-4169
MSC (1991): Primary 57R95, 57R40
Published electronically: May 21, 1999
MathSciNet review: 1637082
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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 $g$, 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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Bang-He Li
Affiliation: Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, Peoples Republic of China

Received by editor(s): March 25, 1998
Published electronically: May 21, 1999
Additional Notes: The author is supported partially by the Tianyuan Foundation of Peoples Republic of China
Article copyright: © Copyright 2000 American Mathematical Society