分野別セミナー

Let us consider a self-transverse immersion of the 2-sphere into 3-space. In 2007, Nowik completely characterized the surfaces that are generated by the complement to the self-intersection set in the 2-sphere for such immersions by constructing immersions explicitly.Furthermore, the author proved the torus version in 2010. In this talk, we show that the sphere immersions constructed by Nowik and new torus immersions corresponding to the immersions constructed by the author are projections of trivial surface knots in 4-space and are regularly homotopic to the standard embeddings in 3-space.