I am rusty on the subject and trying to reconcile this statement (paraphrased from Wikipedia, so likely not precise): "If S is a non-orientable surface, then H1(S) contains a summand Z/2". This is obviously false for a Mobius Strip which has the homotopy type of a circle, so is the disconnect that "surface" really should mean closed (compact without boundary) and the Mobius Strip with or without boundary is not? Thanks all.
2026-04-14 11:17:07.1776165427
Homology of non-orientable surfaces
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