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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
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What are examples when the equality of some invariants is good enough in algebraic topology?
Stiefel-Whitney numbers detect (unoriented) bordism classes and together with Pontryagin numbers, they determine oriented bordism classes.
Ranicki's total surgery obstruction of a finite $n$-dimensio …