A topological interpretation of numbers

Christoforos Neofytidis

A topological interpretation of numbers

Geometric Topology 2026-07-29 v1 Algebraic Topology Group Theory Number Theory

Authors: Christoforos Neofytidis

Abstract

We survey recent advancements on the realisation problem for mapping degree sets. In particular, we explain that any finite set containing zero is the mapping degree set between some $n$ -manifolds, for each $n\geq3$ . Our building factors for the construction of the realising manifolds will be aspherical manifolds. Thus, along the way, we review a couple of open questions related to maps of non-zero degree for aspherical manifolds.

Cite

@article{arxiv.2607.26926,
  title  = {A topological interpretation of numbers},
  author = {Christoforos Neofytidis},
  journal= {arXiv preprint arXiv:2607.26926},
  year   = {2026}
}

Comments

14 pages; survey chapter for the book "Nisyros 2025: Essays in Geometry, History and Philosophy", ed. A. Papadopoulos and S. Yamada