Answer by Ted Shifrin for "Homotopy" group with the torus $\mathbb{T}^2$ as a...
The Hopf Degree Theorem states that if $X$ is a compact, oriented $n$-dimensional manifold, then two (continuous) maps $X\to S^n$ are homotopic if and only if they have the same degree.
View ArticleAnswer by Toyesh Jayaswal for "Homotopy" group with the torus $\mathbb{T}^2$...
I think you can take two loops corresponding to generators of $T^2$ (the 1 cells in the CW decomposition), since $\pi_1$ of $S^2$ is trivial, the images of these loops can be homotoped to a point....
View Article"Homotopy" group with the torus $\mathbb{T}^2$ as a domain and the sphere...
I'm watching this lecture in Condensed Matter physics that concerns topological aspects of materials. In particular, the lecturer is considering the homotopy groups of various spaces. At one particular...
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