The main result of this note (Theorem A) is that the set of piecewise linear (P.L.) manifolds of the same homotopy type as the n-torus, Tn, n ≥ 5, is in one-to-one correspondence with the orbits of An-3(π1Tn) [unk] Z2 under the natural action of the automorphism group of π1Tn. Every homotopy torus has a finite cover P.L. homeomorphic to Tn; hence the generalized annulus conjecture holds in dimension ≥5 (Kirby, R. C., “Stable homeomorphisms,” manuscript in preparation). The methods of this classification are also used to study some conjectures of R. C. Kirby (manuscript in preparation) related to triangulating manifolds.
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机译：该注释（定理A）的主要结果是，与n形同色同构型T n ，n≥5的分段线性（PL）流形的集合位于一个-在π1T n自同构群的自然作用下，与A n-3 （π1T n ）[unk] Z2的轨道一一对应。 sup>。每个同位圆环都有一个有限的覆盖P.L.同胚于T n ;因此，广义的环空猜想的维数≥5（Kirby，R. C.，“稳定的同胚”，准备的手稿）。此分类方法还用于研究R. C. Kirby（正在准备的手稿）中与三角歧管有关的一些猜想。
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