Year: 2026
Type: preprint
Abstract: We construct free immersions of $P^3 \times S^1$ and $S^3 \times S^1$ 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 $m \leq 5$. 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 $\mathrm{SO}(3)$. In our examples, the osculating determinant is constant.
Source: arXiv (Cornell University)
Author: Trinh, Minh-Tâm Quang
Institution: Howard University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214030274