Remarks on tiled tori

Анотація

J. S. Birman and W. W. Menasco [3] introduced and studied a class of embedded tori in closed braid complements which admit a standard tiling. K. Y. Ng showed [6] that each essential torus in a closed braid complement which admits standard tiling posseses a staircase pattern. The combinatorial and geometric description of the tori from this class was partially given in [7]. In this paper, we continue the study of the decomposition of tiled tori into building blocks and show that they are similar in certain sense. In particular, for the class of geometric tiled tori described by Ng in [6], we show that each such torus consists only of elementary blocks.