Inverse limits which are not hereditarily indecomposable

Abstract:

Let $X$ be the limit of an inverse sequence $\left \{ {M_i^n,{f_i}} \right \}$ of closed, connected PL $n$-manifolds with $n \geqslant 2$. It is shown that if either (1) each $M_i^n$ is orientable, each ${f_i}$ has nonzero degree, and ${\sup _i}\left \{ {{\text {rank}}\;{H_1}(M_i^n,{\mathbf {Z}})} \right \} < \infty \;{\text {or}}\;{\text {(2)}}\;{\text {de}}{{\text {g}}_{{\mathbf {Z}}/2{\mathbf {Z}}}}{f_i} \ne 0$ for each $i$ and ${\sup _i}\left \{ {{\text {rank}}\;{H_1}(M_i^n,{\mathbf {Z}}/2{\mathbf {Z}})} \right \} < \infty$, then $X$ is not hereditarily indecomposable.