Year: 2026
Type: preprint
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 $\mathbb R^5$ is nonempty. In particular, every closed surface embeds freely in $\mathbb R^5$. Finally, we find the homotopy invariants of free maps in our environment and study which invariants are achieved by our maps.
Source: arXiv (Cornell University)
Author: De Leo, Roberto
Institution: Howard University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Award: Graphs of Dynamical Systems
OpenAlex ID: W7162452731