File:Simplicial homology - exactness of boundary maps.svg
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Summary
| Description |
English: The boundary of the boundary of a 2-simplex (left) and the boundary of a 1-chain (right) are taken. The boundary of a boundary is always trivial, always sums to 0. A nontrivial cycle is something that closes up like the boundary of a simplex, in that its boundary is 0, but which isn't actually the boundary of a simplex or chain. Two cycles are homologous when their difference is a boundary, and in that sense two closed paths are equivalent if one can turn one into the other by passing through a solid region. |
| Date | |
| Source | Own work |
| Author | Loki Clock |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 01:58, 11 February 2014 | | 260 × 325 (7 KB) | wikimediacommons>LokiClock | Would have to be direct sums of ZZ not direct products to not be misleading, but that would be too big to write in the same place and anyway this is only an isomorphic description, so using the chain groups instead is best. |
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