Fragmented Hofer's geometry

TL;DR

This paper introduces fragmented Hofer's norms, a new class of symplectic metrics controlled by fragmentation norms, and explores their properties and implications in symplectic geometry.

Contribution

It defines and analyzes fragmented Hofer's norms, providing new insights into their structure and relationship with existing symplectic metrics.

Findings

Fragmented Hofer's norms are controlled by fragmentation norms.

Some properties and observations about these norms are established.

Potential implications for symplectic geometry are discussed.

Abstract

Hofer's norm (metric) is an important and interesting topic in symplectic geometry. In the present paper, we define fragmented Hofer's norms which are Hofer's norms controlled by fragmentation norms and give some observations on fragmented Hofer's norms.