Representing nonnegative homology classes of ℂℙ²#𝕟\overline{ℂℙ}² by minimal genus smooth embeddings

Li, Bang-He

doi:10.1090/S0002-9947-99-02422-8

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

Trans. Amer. Math. Soc. 352 (2000), 4155-4169

DOI: https://doi.org/10.1090/S0002-9947-99-02422-8

Published electronically: May 21, 1999

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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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