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The image shows the 4 equivalence classes of the 1st homology on a torus and I was wondering if there was an easy way to check, given any particular homology, whether it was NOT in the trivial equivalence class without any algebra concepts and just geometrically.

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  • $\begingroup$ I think we can just go through each row and add the number of edges and if we ever get an odd number it must not belong to the trivial class. And do the same for the columns. $\endgroup$ – MystMan Aug 14 at 7:51

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