query: What's the name of the surface and Is it a $C^2$ smooth surface?
positive_passages.docid: 22289
positive_passages.text: What's the name of these two surfaces?
negative_passages.docid: 119050
negative_passages.text: Fundamental group of $S^2$ with north and south pole identified
negative_passages.docid: 130189
negative_passages.text: Can quadric surfaces be made by cutting a 4-dimensional cone?
negative_passages.docid: 16647
negative_passages.text: Is the world $C^\infty$?
negative_passages.docid: 38130
negative_passages.text: Complex structure on $\mathbb{C}\mathbb{P}^2\# \dots \# \mathbb{C}\mathbb{P}^2$
negative_passages.docid: 118070
negative_passages.text: Intuitively understanding Riemann surfaces
negative_passages.docid: 154534
negative_passages.text: consider the following subsets of complex plane
negative_passages.docid: 7861
negative_passages.text: Non-analytic smooth function
negative_passages.docid: 57967
negative_passages.text: Difference between $\mathbb C$ and $\mathbb R^2$
negative_passages.docid: 149830
negative_passages.text: What's the name of each pseudo-rectangle in a spherical surface?
negative_passages.docid: 95221
negative_passages.text: Is the cuspidal cubic $\{y^2 = x^3\} \subset \Bbb R^2$ not smooth?
negative_passages.docid: 68234
negative_passages.text: Is $[0,1) \cup \{2\}$ a manifold with boundary? My issue is the $2$.
negative_passages.docid: 78085
negative_passages.text: A non orientable closed surface cannot be embedded into $\mathbb{R}^3$
negative_passages.docid: 80418
negative_passages.text: The "Easiest" non-smoothable manifold
negative_passages.docid: 113919
negative_passages.text: Surface of genus $g$ does not retract to circle (Hatcher exercise)
negative_passages.docid: 118622
negative_passages.text: Local diffeomorphism from $\mathbb R^2$ onto $S^2$
negative_passages.docid: 29304
negative_passages.text: Surface integral of a scalar over a unit cube.