I started reading Morse theory and I learnt one of the fundamental theorem which says that any smooth closed manifold admits a CW complex structure. I had a following question: Given a smooth, closed manifold M, how can we say that in any CW complex structure structure on M, certain dimensional cells must exists? For example, in orientable surfaces with genus greater than 1 we can say that the 1 cells must exist using Euler characteristic argument. What can we say in general?
2026-03-26 06:03:43.1774505023
CW complex structure on manifolds with certain dimensional cells
31 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in SMOOTH-MANIFOLDS
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