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nLab > nLab General Discussions: regular foliation

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    • CommentRowNumber1.
    • CommentAuthorjim stasheff
    • CommentTimeJul 10th 2017
    Searching for definition of `regular foliation' I find several different ones. It is not obvious (to me) they are even equivalent.
    `Leaves having equal dimension' would seem to include Seifert fibrations.
    • CommentRowNumber2.
    • CommentAuthorjim stasheff
    • CommentTimeJul 10th 2017
    Please respond to me directly since I don't check n-forum often enough.
    • CommentRowNumber3.
    • CommentAuthorjim stasheff
    • CommentTimeJul 13th 2017
    Todd provided an excellent review article that compare definitions.
    Nobody seems to know Seifert fibrations.
    They are at least C^1-foliations it seems.
    and NO better than that?
    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 15th 2017

    Just to save possible duplication of effort: the review article Jim refers to in #3 is this.

    And this is what I (essentially) sent him in email a minute ago.

    With regard to your last nForum question, I did spot this: “In 1972 Epstein [E] showed that M has a C^1 foliation by circles if and only if M is a Seifert fibred space.”

    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeJul 28th 2017

    And ‘leaves having equal dimension’ to define ‘regular foliation’ is basically a quote from our article foliation.

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