I have been studying Morse Theory and found something really cool that I have no idea how to prove. The handlebody decomposition of a 2-torus is a 0-handle, two 1-handles, and one 2-handle. Similarly, the handlebody decomposition of a 3-torus is a 0-handle, three 1-handles, three 2-handles and one 3-handle. It seems like it follows Pascal's triangle. Does anyone know if this is true and if so, is there any intuition for this?
2026-03-25 06:12:14.1774419134
Handlebody Decomposition of a torus seems to follow Pascal's triangle
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