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Stable homotopy theory is that part of homotopy theory (and thus algebraic topology) concerned with all structure and phenomena that remain after sufficiently many applications of the suspension functor.

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Does the signature admit a homotopy coherent refinement?

[Since my comment above appears to have been helpful, I am repeating it here.] I must admit I am unfamiliar with L-theory. Nevertheless, I came across a recent article on the arXiv which is related: …
Ricardo Andrade's user avatar