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.
Anderson,The Whitehead torsion of a fiber-homotopy equivalence, Michigan Math
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Simple homotopy types of even dimensional manifolds
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.