Abstract
Lusternik-Schnirelmann category is not well-behaved on products and fibrations. For example, a simple argument shows that for topological spaces Y and Z, max(cat Y, cat Z) ≤ cat(Y × Z) ≤ cat Y + cat Z, and inequalities are sharp: for each one there is a non-trivial example where the inequality is an equality. For general fibrations p: X → Y with fibre F, moreover, the best that can be asserted isKeywordsTopological SpaceCohomology ClassFinite TypeRational HomologyFibre InclusionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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