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Let $X$ be an oriented closed smooth $4$-manifold. Suppose that $TM$ admits a foliation $\mathcal F$ of dimension two, and admits a positvescalar curvature.

Q: If we do the surgery on $X$ to reduce the $b_1$, would the surgery affect the positivity of the scalar curvature on $\mathcal F$.

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  • $\begingroup$ What do you mean by positivity of scalar curvature on $\mathcal{F}$? $\endgroup$
    – Michael Albanese
    Commented Sep 21, 2017 at 13:22
  • $\begingroup$ @MichaelAlbanese scalar curvature of $\mathcal F$ is positive. I mean after the surgery the scalar curvature of $\mathcal F$ is still positive or not. $\endgroup$
    – DLIN
    Commented Sep 21, 2017 at 13:32

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