Minimal genus for 4-manifolds with $b^+=1$

Bo Dai; Chung-I Ho; Tian-Jun Li

doi:10.1112/jtopol/jtv032

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arXiv · 1501.00235

Minimal genus for 4-manifolds with $b^+=1$

Bo Dai·Chung-I Ho·Tian-Jun Li

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Abstract

We derive an adjunction inequality for any smooth, closed, connected, oriented 4-manifold $X$ with $b^+=1$. This inequality depends only on the cohomology algebra and generalizes the inequality of Strle in the case of $b_1=0$. We demonstrate that the inequality is especially powerful when $2\tilde χ+3σ\geq 0$, where $\tilde χ$ is the modified Euler number taking account of the cup product on $H^1$.

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BibTeX RIS

Bo Dai, Chung-I Ho, Tian-Jun Li. 2015-06-21. Minimal genus for 4-manifolds with $b^+=1$. https://doi.org/10.1112/jtopol%2Fjtv032

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