On Steenrod -homology, generalized manifolds, and surgery

The aim of this paper is to show the importance of the Steenrod construction of homology theories for the disassembly process in surgery on a generalized n -manifold X n , in order to produce an element of generalized homology theory, which is basic for calculations. In particular, we show how to construct an element of the n th Steenrod homology group $H^{st}_{n} (X^{n}, \mathbb {L}^+)$ , where 𝕃 + is the connected covering spectrum of the periodic surgery spectrum 𝕃, avoiding the use of the geometric splitting procedure, the use of which is standard in surgery on topological manifolds.