Measure homology and singular homology are isometrically isomorphic
| dc.creator | Loeh, Clara | |
| dc.date | 2005-04-06 | |
| dc.date | 2006-01-30 | |
| dc.date.accessioned | 2026-07-07T06:39:43Z | |
| dc.date.available | 2026-07-07T06:39:43Z | |
| dc.description | Measure homology is a variation of singular homology designed by Thurston in his discussion of simplicial volume. Zastrow and Hansen showed independently that singular homology (with real coefficients) and measure homology coincide algebraically on the category of CW-complexes. It is the aim of this paper to prove that this isomorphism is isometric with respect to the l^1-seminorm on singular homology and the seminorm on measure homology induced by the total variation. This, in particular, implies that one can calculate the simplicial volume via measure homology -- as already claimed by Thurston. For example, measure homology can be used to prove the proportionality principle of simplicial volume. | |
| dc.description | 20 pages, typos corrected, see also http://www.math.uni-muenster.de/u/clara.loeh/preprints.html, accepted by Mathematische Zeitschrift -- the original publication is available at www.springerlink.com (http://dx.doi.org/10.1007/s00209-005-0905-7) | |
| dc.identifier | https://arxiv.org/abs/math/0504103 | |
| dc.identifier | http://arxiv.org/abs/math/0504103 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101182 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Geometric Topology | |
| dc.subject | 55N35 (Primary), 55N10, 57N65 (Secondary) | |
| dc.title | Measure homology and singular homology are isometrically isomorphic | |
| dc.type | text |