Extending a metric on a simplicial complex
Adam Mole
TL;DR
This paper presents a method to extend a metric from vertices to entire simplicial complexes, fixing an error in Mineyev's original flow space construction.
Contribution
It introduces a corrected approach for extending metrics on simplicial complexes, improving upon Mineyev's previous construction.
Findings
Successfully extends vertex metrics to entire complexes.
Corrects a mistake in Mineyev's flow space construction.
Provides a more accurate framework for metric extension.
Abstract
We show how to extend a metric defined on the vertex set of a simplicial complex to the whole simplicial complex, thus correcting a mistake in Mineyev's construction of a flow space.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research