A note on immersed 3-spheres in 4-space

Abstract

There are two special immersed 3--spheres in 4--space, which generate regular homotopy classes of immersed 3--spheres in 4--space. They are constructed with a special sphere eversion called $FM$--eversion. In this note we use geometric approaches to show an immersed 3--sphere in 4--space constructed with $FM$--eversions are not liftable into 5--space.