2008/09/25 by Pierre Derbez, P. Derbez, Derbez, P.
Mathematics · #51H20 #57M50 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:51H20 #msc:57M50
paper · pdf · doi:10.48550/arxiv.0809.4446
arxiv created 2008/09/25 · openalex publication_date 2008/09/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we define, for each aspherical orientable 3-manifold M endowed with a torus splitting Ţ, a 2-dimensional fundamental l1-class [M]Ţ whose l1-norm has similar properties as the Gromov simplicial volume of M (additivity under torus splittings and isometry under finite covering maps). Next, we use the Gromov simplicial volume of M and the l1-norm of [M]Ţ to give a complete characterization of those nonzero degree maps f\co M→ N which are homotopic to a \rm deg(f)-covering map. As an application we characterize those degree one maps f\co M→ N which are homotopic to a homeomorphism in terms of bounded cohomology classes.