Timeline for Are there "geometrically nice" sets from which to construct coverings that admit "Vietoris-Rips like" approximations to the nerve?
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5 events
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| Mar 8, 2013 at 11:01 | comment | added | gspr | @Tim Porter: Oh, I certainly didn't mean equate the role of the nerve with that of the VR complex! What I meant to refer to with the Wikipedia link was simply the relationship between the nerve of a cover by metric balls and the corresponding VR complex. I also apologize for the vagueness of the phrase "other classes of sets". I simply meant "something playing the role of balls in the above-mentioned relationship between the VR complex and the nerve". | |
| Mar 8, 2013 at 10:49 | vote | accept | gspr | ||
| Mar 8, 2013 at 9:50 | comment | added | Tim Porter |
I would disagree with the well known'. The terms nerve and Cech comlex have a wider and older use than just this. The Wikipedia page is not to be trusted. Vietoris complex is also used in a wider and older meaning for an arbitrary covering. Looking at that Wikipedia entry there are numerous inaccuracies. The Cech complex is not dependent on the embedding. Secondly what do you mean byother classes of sets'? Have you investigated Dowker's paper on the homology of relations?
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| Mar 7, 2013 at 20:09 | answer | added | Vidit Nanda | timeline score: 5 | |
| Mar 7, 2013 at 16:07 | history | asked | gspr | CC BY-SA 3.0 |