PreprintarXiv licencearXiv
A topological interpretation of numbers
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≥3. 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.
Related
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BibTeX
@misc{neofytidis2026topological,
title = {{A topological interpretation of numbers}},
author = {Christoforos Neofytidis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.26926},
eprint = {2607.26926},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.26926},
}
RIS
TY - UNPB
TI - A topological interpretation of numbers
AU - Christoforos Neofytidis
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2607.26926
UR - https://arxiv.org/abs/2607.26926
AB - 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≥3. 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.
ER -