two days ago i had an idea: there's a basic non-example for flat chaιns from geοmetric measurε theοry, and i was wondering whether it could be fitted as a counter-example to this conjecture i know.
so far, it's just an idea and very likely, it won't work. as for why it remains an idea ..
two days ago i was still visiting family and had no real time to do any proper thinking. for a day or two my jet lag was still active, though. in the mornings i had about 1 1/2 hours to myself, before anyone woke, to think about mathematics.
yesterday i was traveling (unfortunately) for most of the day. by the time i arrived home, i was in no mood to work. besides, a friend and colleague was leaving, and i promised to meet him at the bar.
i thought a little about that idea today, worked out some details. i was right: it won't work .. not as formulated.
i learned something, though -- that there is some rigidity in how the induced vectοrfield behaves on a flat chaιn. (roughly speaking, flat chaιns are geometric objects with additional information; like many smooth manifolds, they can admit something like a "generalised οrientation.")
i don't feel like editing preprints today, anyway, so i might as well see exactly how rigid these choices can be, and how this can relate to the aforementioned conjecture ..
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