From Heegaard splittings to trisections; porting 3-dimensional ideas to dimension 4
Geometric Topology
2019-02-06 v1
Abstract
These notes summarize and expand on a mini-course given at CIRM in February 2018 as part of Winter Braids VIII. We somewhat obsessively develop the slogan `Trisections are to 4-manifolds as Heegaard splittings are to 3-manifolds', focusing on and clarifying the distinction between three ways of thinking of things: the basic definitions as decompositions of manifolds, the Morse theoretic perspective and descriptions in terms of diagrams. We also lay out these themes in two important relative settings: 4-manifolds with boundary and 4-manifolds with embedded 2-dimensional submanifolds.
Keywords
Cite
@article{arxiv.1902.01797,
title = {From Heegaard splittings to trisections; porting 3-dimensional ideas to dimension 4},
author = {David T. Gay},
journal= {arXiv preprint arXiv:1902.01797},
year = {2019}
}
Comments
28 pages, 9 figures, notes from mini-course at Winter Braids VIII, School on Braids and Low-dimensional Topology