# Extensions of immersions of surfaces into $\mathbb{R}^{3}$

## TL;DR

This paper classifies all equivalence classes of immersed 3-manifolds bounded by a given immersed surface in three-dimensional space, extending previous work to a broader class of surfaces.

## Contribution

It provides a complete classification of immersed 3-manifolds bounded by arbitrary immersed surfaces in , generalizing earlier results.

## Key findings

- All equivalence classes of such 3-manifolds are determined.
- The classification applies to arbitrary immersed surfaces, not just simple or convex ones.
- The work extends the understanding of surface immersions in .

## Abstract

This paper is to study the $\mathbb{R}^{3}$ case of \hyperref[Zhao]{[9]}. We determine all equivalence classes of immersed $3$-manifolds bounded by an arbitrary immersed surface in $\mathbb{R}^{3}$.