This question is of no real consequence, it just popped into my head and I am curious about it.

Apple uses a file format called the .sparsebundle for Time Machine backups on network drives. A sparsebundle is basically a disk image that expands as more data is added to it; it's functionally equivalent to a .sparseimage, except that it is specifically used for keeping backups of multiple computers together but separate. (I know it's probably more technical than that; don't @ me).

Anyway it occurred to me today that both "sparse" and "bundle" get a lot of use in mathematics. We have sparse matrices, sparse graphs, sparse solutions, etc., and we have tangent bundles, normal bundles, fiber bundles, etc. But candidly, I don't know enough about any of those contexts to know if it would ever make sense to use the two words together.

Does the phrase "sparse bundle" mean anything in mathematics? If so, what?

  • $\begingroup$ Also, if someone thinks this needs the soft-question tag, feel free to add it. I feel like this has an answer and is not opinion-based so I left it off but I would not object. $\endgroup$ – mweiss Nov 15 '18 at 19:51

Probably not (yet): a quick search of the arxiv shows only 30 articles that have both the words "sparse" and "bundle" anywhere in any of the metadata, and none of them have the words glued together like that ;)


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