query: Is the following $f:S^3 \rightarrow S^2$ a submersion?
positive_passages.docid: 154496
positive_passages.text: Proving that the Hopf map $S^3 \to S^2$ is a submersion
negative_passages.docid: 107609
negative_passages.text: Function whose third derivative is itself.
negative_passages.docid: 118622
negative_passages.text: Local diffeomorphism from $\mathbb R^2$ onto $S^2$
negative_passages.docid: 19399
negative_passages.text: $f^2$ and $f^3$ are holomorphic implies $f$ is holomorphic.
negative_passages.docid: 22297
negative_passages.text: Normal operator $\Rightarrow$ S invariant implies $S^\perp$ invariant
negative_passages.docid: 147310
negative_passages.text: How does one prove that the Klein bottle cannot be embedded in $R^3$?
negative_passages.docid: 84389
negative_passages.text: Topologist's Sine Curve not a regular submanifold of $\mathbb{R^2}$?
negative_passages.docid: 92033
negative_passages.text: Prove that $g$ is a submanifold: $g (t,u,v) = (t^2,u^2,v^2,\sqrt{2}uv, \sqrt{2}tv,\sqrt{2}tu)$
negative_passages.docid: 121886
negative_passages.text: Proving image of $f:D^n\rightarrow \mathbb{R}^n \;$ contains $\;D^n$
negative_passages.docid: 24828
negative_passages.text: surjective immersion $\mathbb{R}^2 \to \mathbb{R}^2$ which is not a diffeomorphism
negative_passages.docid: 64381
negative_passages.text: Prove that if one of $\lim_{x \rightarrow 0 }{f(x)}$ and $\lim_{x \rightarrow 0}{f(x^3)}$ exists, then the other one also exists.
negative_passages.docid: 48127
negative_passages.text: Are there infinitely many $A\in \mathbb{C}^{2 \times 2}$ satisfying $A^3 = A$?
negative_passages.docid: 112807
negative_passages.text: Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
negative_passages.docid: 36700
negative_passages.text: Quotient space of closed unit ball and the unit 2-sphere $S^2$
negative_passages.docid: 72115
negative_passages.text: Why isn't there a continuously differentiable surjection from $I \to I \times I$?
negative_passages.docid: 82458
negative_passages.text: Homeomorphism between the unit disc and the unit square
negative_passages.docid: 39453
negative_passages.text: How do I prove that $S^n$ is homeomorphic to $S^m \Rightarrow m=n$?