How do I construct a torus as a cell structure?
Visually I do not think I quite see the construction. Furthermore, how do I construct a 3-holed torus, that is, a 3 genus surface as a cell structure?
2026-03-28 04:33:39.1774672419
Cell Structure of Three holed torus
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If you glue a torus from a square, you can take the square to be the 2-cell, the edges to be its two 1-cells, and its vertices to be the one 0-cell.
A genus-3 surface is a connect sum of three tori. You can make an identification diagram by cutting out a disk in a two-cell in each of the diagrams and pasting them together along the boundaries. Then, to get a cell structure, you cut any 2d region that isn't just a disk.