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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1969 Mar;62(3):687–691. doi: 10.1073/pnas.62.3.687

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

W C Hsiang 1, J L Shaneson 1
PMCID: PMC223652  PMID: 16591738

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, Tn, n ≥ 5, is in one-to-one correspondence with the orbits of An-31Tn) [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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