PreprintCC BY 4.0arXiv
Free Immersions in Critical Dimension from Lie Groups
Abstract
We construct free immersions of P3 × S1 and S3 × S1 into $14$-space. These are the first examples of free immersions in critical dimension of closed manifolds that are not spheres, projective spaces, tori, or surfaces. The idea is to mimic De Leo's construction for m-tori with m ≤ 5. De Leo constructs a map that is symmetric with respect to a representation of the Lie group formed by the $(m - 1)$-torus; we replace this group with SO(3). In our examples, the osculating determinant is constant.
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BibTeX
@misc{trinh2026free,
title = {{Free Immersions in Critical Dimension from Lie Groups}},
author = {Minh-Tâm Quang Trinh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24777},
eprint = {2609.24777},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24777},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Free Immersions in Critical Dimension from Lie Groups
AU - Minh-Tâm Quang Trinh
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.24777
UR - https://arxiv.org/abs/2609.24777
AB - We construct free immersions of P^3 × S^1 and S^3 × S^1 into $14$-space. These are the first examples of free immersions in critical dimension of closed manifolds that are not spheres, projective spaces, tori, or surfaces. The idea is to mimic De Leo's construction for m-tori with m ≤ 5. De Leo constructs a map that is symmetric with respect to a representation of the Lie group formed by the $(m - 1)$-torus; we replace this group with SO(3). In our examples, the osculating determinant is constant.
ER -