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Jan 31, 2014 at 13:54 comment added Ricardo Andrade I just want to make a couple of tangential remarks about this result of Kirby and Siebenmann. First, their result is much finer and harder than the statement that manifolds have the homotopy types of CW-complexes. A celebrated generalization of this result is Borsuk's conjecture that compact ANRs have the homotopy type of finite CW-complexes, which was finally proved by James West and announced in Compact ANR's have finite type (Bull. Amer. Math. Soc. Volume 81, Number 1, 1975, pages 163-165).
Jan 31, 2014 at 13:36 history answered Danny Ruberman CC BY-SA 3.0