Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

HOME ALL ARTICLES View

J. Korean Math. Soc. 2004; 41(4): 591-615

Printed July 1, 2004

Copyright © The Korean Mathematical Society.

Foundations of the theory of $\ell_{1}$ homology

HeeSook Park

Vassar College

Abstract

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

Stats or Metrics

Share this article on :

Related articles in JKMS