Exotic finite functorial semi-norms on singular homology

TL;DR

This paper introduces new finite functorial semi-norms on singular homology that differ from the classical l^1-semi-norm, providing refined measures of homology classes.

Contribution

It demonstrates the existence of exotic finite functorial semi-norms on singular homology not derived from the l^1-semi-norm.

Findings

Existence of finite functorial semi-norms different from l^1-semi-norm

These semi-norms provide alternative size measures for homology classes

They are not dominated by the l^1-semi-norm

Abstract

Functorial semi-norms on singular homology give refined "size" information on singular homology classes. A fundamental example is the l^1-semi-norm. We show that there exist finite functorial semi-norms on singular homology that are exotic in the sense that they are not carried by the l^1-semi-norm.