2005/04/06 by Clara Loeh, Loeh, Clara · 3 citations
Computer Science · Mathematics · Medicine · #55N10 #55N35 (Primary) #57N65 (Secondary) #Advanced Neuroimaging Techniques and Applications #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.GT #msc:55N10 #msc:55N35 #msc:57N65
paper · pdf · doi:10.48550/arxiv.math/0504103
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)
openalex publication_date 2005/04/06 · arxiv created 2006/01/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 l1-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.