A topological interpretation of numbers
arXiv:2607.26926
The paper surveys recent results showing that any finite set containing zero can be realized as the set of mapping degrees between some n‑manifolds (for n ≥ 3), using constructions based on aspherical manifolds, and discusses related open questions.
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 -manifolds, for each . 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.
14 pages; survey chapter for the book "Nisyros 2025: Essays in Geometry, History and Philosophy", ed. A. Papadopoulos and S. Yamada