2021/01/29 by Mattia Magnabosco, Magnabosco, Mattia
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.DG #math.MG
paper · pdf · doi:10.48550/arxiv.2102.00042
arxiv created 2021/01/29 · arxiv updated 2021/02/02
Ketterer and Rajala showed an example of metric measure space, satisfying the measure contraction property MCP(0,3), that has different topological dimensions at different regions of the space. In this article I propose a refinement of that example, which satisfies the CD(0,∞) condition, proving the non-constancy of topological dimension for CD spaces. This example also shows that the weak curvature dimension bound, in the sense of Lott-Sturm-Villani, is not sufficient to deduce any reasonable non-branching condition. Moreover, it allows to answer to some open question proposed by Schultz, about strict curvature dimension bounds and their stability with respect to the measured Gromov Hausdorff convergence.