Cubulated moves for 2-knots

Abstract

In this paper, we prove that given two cubical links of dimension two in ${\mathbb{R}}^4$, they are isotopic if and only if one can pass from one to the other by a finite sequence of cubulated moves. These moves are analogous to the Reidemeister and Roseman moves for classical tame knots of dimension one and two, respectively.

arXiv comment9 figures. arXiv admin note: text overlap with arXiv:1302.2133