Metric Properties and Distortion in Wreath Products
Jos\'e Burillo, Eric L\'opez-Plat\'on
TL;DR
This paper introduces a polynomial-time metric estimate for regular wreath products, explores subgroup distortion, and extends the estimate to nonregular cases, addressing computational complexity issues.
Contribution
It provides a new polynomial-time metric estimate for regular wreath products and generalizes it to nonregular cases, improving understanding of their metric properties.
Findings
Polynomial-time metric estimate for regular wreath products
Analysis of subgroup distortion within wreath products
Extension of metric estimates to nonregular wreath products
Abstract
For a finitely generated regular wreath product, the metric is known, but its computation can be an NP-complete problem. Also, it is not known for the nonregular case. In this article, a metric estimate is defined for regular wreath products which can be computed in polynomial time, based on the metrics of the factors. This estimate is then used to study the distortion of some natural subgroups of a wreath product. Finally, the metric estimate is generalized to the nonregular case.
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Taxonomy
TopicsGeometric and Algebraic Topology · Numerical methods in engineering · Soft tissue tumor case studies