Universal finite functorial semi-norms
Category Theory
2024-07-04 v2 Algebraic Topology
Abstract
Functorial semi-norms on singular homology measure the "size" of homology classes. A geometrically meaningful example is the -semi-norm. However, the -semi-norm is not universal in the sense that it does not vanish on as few classes as possible. We show that universal finite functorial semi-norms do exist on singular homology on the category of topological spaces that are homotopy equivalent to finite CW-complexes. Our arguments also apply to more general settings of functorial semi-norms.
Cite
@article{arxiv.2209.12971,
title = {Universal finite functorial semi-norms},
author = {Clara Loeh and Johannes Witzig},
journal= {arXiv preprint arXiv:2209.12971},
year = {2024}
}
Comments
v2: small improvements/correction of typos; 16 pages; to appear in Applied Categorical Structures