J. Korean Math. Soc. 2004; 41(4): 591-615
Printed July 1, 2004
Copyright © The Korean Mathematical Society.
HeeSook Park
Vassar College
In this paper, we provide the algebraic foundations to the theory of relative $\ell_{1}$ homology. In particular, we prove that \( \ell_{1} \) 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 $\ell_{1}$ homology, stated by Gromov without proof [4].
Keywords: $\ell_{1}$ homology, relative $\ell_{1}$ homology
MSC numbers: Primary 55N35; Secondary 55U99, 20J06
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