query: There is a smooth map of degree 1 from $S^1 \times S^1$ to $S^2$
positive_passages.docid: 154303
positive_passages.text: Degree $1$ map from torus to sphere
negative_passages.docid: 63836
negative_passages.text: Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective
negative_passages.docid: 20383
negative_passages.text: True or False: there is a space $X$ such that $S^1$ is homeomorphic to $X\times X$
negative_passages.docid: 152725
negative_passages.text: Why does $S^n$ satisfy the local $n$-slice condition? (From Lee's Smooth Manifolds)
negative_passages.docid: 157002
negative_passages.text: Connected compact covering space of torus is homeomorphic to $S^1\times S^1$
negative_passages.docid: 154837
negative_passages.text: mapping properties of $(1−z)^i$
negative_passages.docid: 45276
negative_passages.text: Continuous map on $S^2$
negative_passages.docid: 153052
negative_passages.text: What does the degree of a loop in $S^1$ means *intuitively?
negative_passages.docid: 44559
negative_passages.text: Finding a homeomorphism $\mathbb{R} \times S^1 \to \mathbb{R}^2 \setminus \{(0,0)\}$
negative_passages.docid: 44069
negative_passages.text: Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
negative_passages.docid: 40858
negative_passages.text: Multiplicative nature of the separability degree
negative_passages.docid: 15095
negative_passages.text: continuous onto map from $(0,1)\to (0,1]$
negative_passages.docid: 100736
negative_passages.text: Why every map $f : S^n \to T^n (n>1)$ has topological degree zero?
negative_passages.docid: 52517
negative_passages.text: Construction of $\mathbb{CP}^2$ from $S^2\times S^2$
negative_passages.docid: 8799
negative_passages.text: Mapping homotopic to the identity map has a fixed point
negative_passages.docid: 132063
negative_passages.text: locally on $S$ one of the coordinates is a $C^∞$ function of the other coordinate. Show that $S$ is a submanifold of $R^2$
negative_passages.docid: 40490
negative_passages.text: Birational isomorphism $\mathbb{P}^n\times \mathbb{P}^m\to \mathbb{P}^{n+m}$