Math gifts

- Art Gallery -

The Hopf theorem (named after Heinz Hopf) is a statement in differential topology, saying that the topological degree is the only homotopy invariant of continuous maps to spheres.

Formal statement

Let M be an n-dimensional compact oriented manifold and \( S^{n} \) the n-sphere and \( {\displaystyle f,g\colon M\to S^{n}} \) be continuous. Then \( \deg(f)=\deg(g) \) if and only if f and g are homotopic.

Milnor, John W. (1997). Topology from the Differentiable Viewpoint. Princeton University Press. ISBN 978-0-691-04833-8.

Undergraduate Texts in Mathematics

Graduate Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia



Hellenica World - Scientific Library

Retrieved from ""
All text is available under the terms of the GNU Free Documentation License