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nLab > Latest Changes: lens space

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJul 22nd 2020

    Page created, but author did not leave any comments.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 22nd 2020

    needed to record a reference. Now somebody needs to put some content into this entry… :-)

    v1, current

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 22nd 2020

    Link to Manifold Atlas.

    diff, v2, current

  4. Added some content to the idea section.

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorRichard Williamson
    • CommentTimeJul 22nd 2020
    • (edited Jul 22nd 2020)

    In particular, added a construction (with picture in tikz, for my sins!) of lens spaces via integral surgery, which, though completely standard, is not that easy to find in the literature if one does not know where to look.

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 18th 2020

    added this pointer:

    • Michel Boileau, Steven Boyer, Radu Cebanu, Genevieve S. Walsh, Section 3 of: Knot commensurability and the Berge conjecture, Geom. Topol. 16 (2012) 625-664 (arXiv:1008.1034)

    diff, v5, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 18th 2020
    • (edited Nov 18th 2020)

    added pointer on 3d-3d correspondence for lens spaces:

    diff, v5, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeNov 18th 2020

    I have added the actual definition to the entry and have organized the previous material into subsections of a “Properties” section.

    The paragraph on Dehn surgery seemed to have been lacking the qualifier “coprime”, so I added it.

    diff, v5, current

    • CommentRowNumber9.
    • CommentAuthorRichard Williamson
    • CommentTimeNov 18th 2020
    • (edited Nov 18th 2020)

    Thanks for the correction! Regarding

    are in some sense the simplest

    there is at least one precise sense in which this is true, namely Lens spaces are the only 3-manifolds one can obtain by integral Dehn surgery on the unknot except for S 3S^{3} and  S 2×S 1S^{2} \times S^{1}. In a hurry now, so no time to find a reference, but it might be nice to add this to the entry; it should be in any textbook on geometric topology.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeNov 18th 2020

    Okay. I have added the “in some sense” only to make clear that at this point it’s an informal statement. But if it can be made precise further down in the entry, all the better.

  11. Added two main theorems for classification concerning when lens spaces are homeomorphic and homotopy equivalent.

    diff, v7, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeFeb 15th 2024

    I moved all the primes to before the subscripts, for them to render at the expected spot

    diff, v8, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2024

    added pointer to:

    • Laurentio-George Maxim, Cohomology of Lens Spaces [pdf]

    diff, v9, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2024

    added pointer to:

    diff, v10, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2024

    added the statement of the ordinary integral cohomology of lens spaces (here)

    diff, v10, current

1 to 15 of 15

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