2009/01/15 by Chad Groft, Groft, Chad
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #20F65 (secondary) #53C23 (primary) #Chemical Synthesis and Analysis #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #math.GT #msc:20F65 #msc:53C23 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0901.2303
19 pages
arxiv created 2009/01/15 · openalex publication_date 2009/01/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a finite CW complex or compact Lipschitz neighborhood retract with universal cover Z; let M be a compact orientable manifold of dimension at least 2 and nonempty boundary. We establish the existence of an isoperimetric profile for functions from M to Z, in the metric and cellular senses, and show that they are equivalent up to scaling factors when X is a triangulated CLNR (for example a triangulated Riemannian manifold). This seems to be most interesting when X is highly connected, but this is not required. We also show that two finite complexes X and Y have the same profiles up to scaling given the existence of a sufficiently connected map between them.