English

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 1\ell^1-semi-norm. However, the 1\ell^1-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.

Keywords

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

R2 v1 2026-06-28T02:08:45.099Z