I read in Hatcher's "Algebraic topology" book about orientability of topological maifolds using homology. now I would like to know how one can apply this to show that the möbius strip is not orientable? i have no idea.
orientability of the möbius strip using homology
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geometry
general-topology
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1A connected $n$-manifold is orientable iff $H_n(M,\partial M)\cong\mathbb Z$. – 2012-05-16
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0how can one prove this? or is it in hatcher's book, at whic page? – 2012-05-16
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4See Theorem 3.43 of Hatcher. – 2012-05-16
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0@Jim - Surely this should be an answer? :) – 2012-05-17