Rank gradient and p-gradient of amalgamated free products and HNN extensions
Nathaniel Pappas
TL;DR
This paper computes the rank gradient and p-gradient for free products, amalgamated free products, and HNN extensions with amenable subgroups, using cost and subgroup theorems to derive explicit formulas.
Contribution
It provides explicit calculations of rank and p-gradients for complex group constructions involving amalgamation and HNN extensions, expanding understanding of their subgroup properties.
Findings
Calculated rank gradient for amalgamated free products and HNN extensions.
Derived p-gradient formulas using Kurosh subgroup theorems.
Connected cost to rank gradient in these group constructions.
Abstract
We calculate the rank gradient and p-gradient of free products, free products with amalgamation over an amenable subgroup, and HNN extensions with an amenable associated subgroup. The notion of cost is used to compute the rank gradient of amalgamated free products and HNN extensions. For the p-gradient the Kurosh subgroup theorems for amalgamated free products and HNN extensions will be used.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows