2021/12/22 by Clara Loeh, Loeh, Clara, Marco Moraschini +3 · 1 citation
Mathematics · #28D15 (Secondary) #55N10 (Primary) 55N35 #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2112.12223
openalex publication_date 2021/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In analogy with ordinary simplicial volume, we show that integral foliated simplicial volume of oriented closed connected aspherical n-manifolds that admit an open amenable cover of multiplicity at most n is zero. This implies that the fundamental groups of such manifolds have fixed price and are cheap as well as reproves some statements about homology growth.