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Jan 22, 2022 at 22:51 comment added Sam Nead This is a nice question. I makes me wonder about the possibility of a further "promotion" - once the loop is transverse, might it also have lots of friends, in the form of a flow?
Jan 22, 2022 at 6:58 answer added Ian Agol timeline score: 2
Jan 20, 2022 at 4:01 comment added Ian Agol Not really an answer, but I think if a loop can be homotoped to be transverse to the taut foliation, then it ought to act by a non-trivial translation on the leaf space of the pullback of the taut foliation to the universal cover, which is a non-hausdorff simply-connected 1-manifold. I think that the converse might also be true. mathscinet.ams.org/mathscinet-getitem?mr=1969207
S Nov 17, 2021 at 2:02 history bounty ended CommunityBot
S Nov 17, 2021 at 2:02 history notice removed CommunityBot
S Nov 9, 2021 at 0:40 history bounty started Audrey Rosevear
S Nov 9, 2021 at 0:40 history notice added Audrey Rosevear Draw attention
Nov 3, 2021 at 1:04 history asked Audrey Rosevear CC BY-SA 4.0