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I am confused by the orientation convention that Ozsvath and Szabo use in On Heegaard Floer homology and Seifert Fibered Surgeries and would appreciate if someone clarifies this for me. On page 15 there is a

Definition 3.1 Suppose that $\Gamma$ is a weighted tree which has either negative-definite or negative-semi-definite intersection form. Then, we say that the induced orientation $-\partial W(\Gamma)$ is a positive Seifert orientation.

I am confused by the use of "induced orientation" together with a minus sign after it. It seems that there is a double negation going on. Is that true? More precisely, does this definition say:

Let $Y$ be a Seifert fibred space that bounds a positive definite 4-manifold obtained by plumbing, Then $Y$ has positive Seifert orientation. If $Y$ is a Seifert fibred space that bounds a negative definite 4-manifold obtained by plumbing, Then $Y$ has negative Seifert orientation. (Can have both.) Is this correct?

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  • $\begingroup$ Yes, it appears to say so. Is this not consistent with their results? $\endgroup$ – Marco Golla Oct 21 '14 at 14:51
  • $\begingroup$ @MarcoGolla: No, I don't know if it is inconsistent or not. I just wanted to make sure I understand this correctly. The double negation is what confuses me and makes me unsure whether I understand it correctly. $\endgroup$ – shestipalov Oct 22 '14 at 8:59

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