PreprintCC BY 4.0arXiv
Topological point singularities of manifold-valued maps and approximability by smooth maps
Abstract
Given a positive integer~p, we consider W1,p-maps from a Euclidean domain of dimension p+1 into a closed Riemannian manifold NN. The target manifold is required to satisfy a suitable topological condition, that is, the action of the fundamental group over the~p-th homotopy group must be trivial; however, we do \emph{not} assume that NN is (p−1)-connected. Using tools from geometric measure theory --- namely, chains with coefficients in the p-th homotopy group of~NN--- we associate to each map a new object that captures its topological point singularities. We provide a characterisation of strong and weak sequential closures of smooth maps in~W1,p in terms of their topological singularities.
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BibTeX
@misc{canevari2026topological,
title = {{Topological point singularities of manifold-valued maps and approximability by smooth maps}},
author = {Giacomo Canevari and Giandomenico Orlandi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.28622},
eprint = {2605.28622},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.28622},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Topological point singularities of manifold-valued maps and approximability by smooth maps
AU - Giacomo Canevari
AU - Giandomenico Orlandi
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2605.28622
UR - https://arxiv.org/abs/2605.28622
AB - Given a positive integer~p, we consider W^1,p-maps from a Euclidean domain of dimension p+1 into a closed Riemannian manifold NN. The target manifold is required to satisfy a suitable topological condition, that is, the action of the fundamental group over the~p-th homotopy group must be trivial; however, we do \emph{not} assume that NN is (p−1)-connected. Using tools from geometric measure theory --- namely, chains with coefficients in the p-th homotopy group of~NN--- we associate to each map a new object that captures its topological point singularities. We provide a characterisation of strong and weak sequential closures of smooth maps in~W^1,p in terms of their topological singularities.
ER -