Low-dimensional Examples
The low-dimensional examples of homotopy groups of spheres provide a sense of the subject, because these special cases can be visualized in ordinary 3-dimensional space (Hatcher 2002). However, such visualizations are not mathematical proofs, and do not capture the possible complexity of maps between spheres.
Read more about this topic: Homotopy Groups Of Spheres
Famous quotes containing the word examples:
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (15331592)