An indecomposable \(PD_3\)-complex. II (Q1766293)

In the paper reviewed below [Math. Proc. Camb. Philos. Soc. 138, No. 1, 55--57 (2005; Zbl 1067.57016)] the author showed that \(S_{3} * _{\mathbb Z/2\mathbb Z} S_{3}\) satisfies \textit{V. G. Turaev's} condition [Math. USSR, Sb. 67, No.~1, 261--282 (1990); translation from Mat. Sb. 180, No.~6, 809--830 (1989; Zbl 0717.57008)] to be the fundamental group of an orientable Poincaré 3-complex. This gives an example of an indecomposable Poincaré 3-complex with a fundamental group with infinitely many ends. In this paper the author constructs two homotopically distinct Poincaré 3-complexes with this fundamental group. The double covers of these spaces are homotopy equivalent to \(L(3,1) \sharp L(3,1)\) and \(L(3,1) \sharp -L(3,1)\).