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Let $Y$ be an oriented closed $3$-manifold, with trivial homology group, i.e. integer homological sphere.

Q: If $Y$ can be embedded into $\mathbb R^4$, is there any example, that such a $Y$ admits a negative scalar curvature?

Let $Y$ be an oriented closed $3$-manifold, with trivial homology group, i.e. integer homological sphere.

Q: If $Y$ can be embedded into $\mathbb R^4$, is there any example, that such a $Y$ admits a negative scalar curvature?

Let $Y$ be an oriented closed $3$-manifold, with trivial homology group, i.e. integer homological sphere.

Q: If $Y$ can be embedded into $\mathbb R^4$, is there any example, that such a $Y$ admits a negative scalar curvature?

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DLIN
DLIN
  • 1.9k
  • 1
  • 10
  • 19

Homology Sphere Embedding into $\mathbb R^4$

Let $Y$ be an oriented closed $3$-manifold, with trivial homology group, i.e. integer homological sphere.

Q: If $Y$ can be embedded into $\mathbb R^4$, is there any example, that such a $Y$ admits a negative scalar curvature?