Uniqueness of surface diagrams of smooth 4-manifolds
Abstract
In the author's earlier work there appeared a new way to specify any smooth closed 4-manifold by a surface diagram, which consists of an orientable surface decorated with simple closed curves. These curves are cyclically indexed, and each curve has a unique transverse intersection with the next. Each surface diagram comes from a certain type of map from the 4-manifold to the two-sphere. The aim of this paper is to give a uniqueness theorem stating that surface diagrams coming from maps within a fixed homotopy class are unique up to four moves: stabilization, handleslide, multislide, and shift.
Keywords
Cite
@article{arxiv.1103.6263,
title = {Uniqueness of surface diagrams of smooth 4-manifolds},
author = {Jonathan D. Williams},
journal= {arXiv preprint arXiv:1103.6263},
year = {2018}
}
Comments
Informal material added for readability in numerous places and many details and intermediate steps added to the later arguments in response to referee comments; references updated. 62 pages, many figures