| Abstract: | Gross and Rosen asked if the genus of a 2-dimensional complex K embeddable in some (orientable) surface is equal to the genus of the graph of appropriate barycentric subdivision of K. We answer the nonorientable genus and the Euler genus versions of Gross and Rosen's question in affirmative. We show that this is not the case for the orientable genus by proving that taking ⌊ log2 g⌋ th barycentric subdivision is not sufficient, where g is the genus of K. On the other hand, (1+⌈log2(g+2)⌉)th subdivision is proved to be sufficient. © 1997 John Wiley & Sons, Inc. |
