On the singular homology of one class of simply-connected cell-like spaces (Q545468)

A Warsaw circle (the closed-up topologist's sine curve) is a non-contractible planar continuum, all of whose homotopy groups vanish. \textit{V. Karimov} and \textit{D. Repovš} [Proc. Am. Math. Soc. 138, No.~4, 1525--1531 (2010; Zbl 1196.54057)], found a non-contractible, homology locally connected continuum, with vanishing homotopy groups. But this is infinite dimensional. The present authors, [Fundam. Math. 195, No.~3, 193--203 (2007; Zbl 1148.54016)] constructed a functor \(SC(-,-)\) by gluing a cylinder to a square along an open topologist's sine curve. They called \(SC(Z,*)\) the Snake cone, and \(SC(S^1,*)\) the Snake space. The goals of the present paper are 1) to give a simple proof that the Snake cone on a path connected space is simply-connected and 2) to show that if \(Z\) is \((n-1)\) connected, \(n\geq 2\), then \(Hn(SC(Z);{\mathbb Z})\) and \(\pi_n(SC(Z),z_0)\) are trivial.