Type: Article
Publication Date: 2004-07-01
Citations: 8
DOI: https://doi.org/10.4134/jkms.2004.41.4.591
In this paper, we provide the algebraic foundations to the theory of relative <TEX>$\ell$</TEX><TEX>$_1$</TEX> homology. In particular, we prove that <TEX>$\ell$</TEX><TEX>$_1$</TEX> homology of topological spaces, both for the absolute case and for the relative case, depends only on their fundamental groups. We also provide a .proof of Gromov's Equivalence theorem for <TEX>$\ell$</TEX><TEX>$_1$</TEX> homology, stated by Gromov without proof [4].