Geodesic
Invariance of Torsion and the Borsuk Conjecture
Canadian journal of mathematics, Tome 32 (1980) no. 6, pp. 1333-1341

Voir la notice de l'article provenant de la source Cambridge University Press

The following results of Whitehead and Wall are well-known applications of the algebraic K-theoretic functors K 0 and K 1 to basic homotopy questions in topology.THEOREM 1 [20]. If f : X → Y is a homotopy equivalence between compact CW complexes, then there is a torsion τ(ƒ) in the algebraically-defined Whitehead group Wh π1(Y) which vanishes if and only if f is a simple homotopy equivalence.THEOREM 2 [18]. If X is an arbitrary space which is finitely dominated (i.e., homotopically dominated by a compact polyhedron), then there is an obstruction σ(X) in the algebraically-defined reduced projective class group which vanishes if and only if X is homotopy equivalent to some compact polyhedron.If we direct sum over components, then the above statements make good sense even if the spaces involved are not connected. 
Chapman, T. A. Invariance of Torsion and the Borsuk Conjecture. Canadian journal of mathematics, Tome 32 (1980) no. 6, pp. 1333-1341. doi: 10.4153/CJM-1980-103-5
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