PreprintCC BY-NC-ND 4.0arXiv
Free maps in critical dimension on low-dimensional tori and closed surfaces
Abstract
We present a method to build free immersions in critical dimension on m-tori for m = 2, 3, 4, 5 by using a factorization trick inspired by tori immersions in critical dimension. As an application, we show that the set of smooth free maps from a closed surface M to ℝ5 is nonempty. In particular, every closed surface embeds freely in ℝ5. Finally, we find the homotopy invariants of free maps in our environment and study which invariants are achieved by our maps.
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BibTeX
@misc{leo2026free,
title = {{Free maps in critical dimension on low-dimensional tori and closed surfaces}},
author = {Roberto De Leo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.24610},
eprint = {2605.24610},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.24610},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Free maps in critical dimension on low-dimensional tori and closed surfaces
AU - Roberto De Leo
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2605.24610
UR - https://arxiv.org/abs/2605.24610
AB - We present a method to build free immersions in critical dimension on m-tori for m = 2, 3, 4, 5 by using a factorization trick inspired by tori immersions in critical dimension. As an application, we show that the set of smooth free maps from a closed surface M to ℝ^5 is nonempty. In particular, every closed surface embeds freely in ℝ^5. Finally, we find the homotopy invariants of free maps in our environment and study which invariants are achieved by our maps.
ER -