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Results tagged with homotopy-theory
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user 26595
Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
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Does the reduced Mapping cylinder have the same homotopy type of unreduced Mapping cylinder?
Let $ f:X\to Y $ be a map in the pointed category of topological spaces $ Top_* $. And let $ U:Top_*\to Top $ be the "forgetful" functor (which "forgets" the basepoint). We can look at the reduced map …
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