Existence of non-free stably free Swan module resolves Wall Problem A4 and yields homotopy inequivalent n-complexes after single vs multiple stabilizations when n ≡ 3 mod 4.
[Oli88] Robert Oliver,Whitehead groups of finite groups, London Mathematical Society Lecture Note Series, vol
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The authors characterize the simple homotopy manifold set via algebraic K-theory and surgery obstructions, then construct infinite families of even-dimensional manifolds homotopy equivalent to S^1 times a lens space that are pairwise not simple homotopy equivalent.
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Swan modules and homotopy types after a single stabilisation
Existence of non-free stably free Swan module resolves Wall Problem A4 and yields homotopy inequivalent n-complexes after single vs multiple stabilizations when n ≡ 3 mod 4.