FAKE TORI, THE ANNULUS CONJECTURE, AND THE CONJECTURES OF KIRBY

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Abstract
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, T(n), n >/= 5, is in one-to-one correspondence with the orbits of A(n-3)(pi(1)T(n)) [unk] Z(2) under the natural action of the automorphism group of pi(1)T(n). Every homotopy torus has a finite cover P.L. homeomorphic to T(n); 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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