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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 24th 2018

    Presently this entry has much overlap with Clifford-Klein space form and group actions on spheres. Eventually the three will diverge.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 25th 2018

    Fine-tuned and corrected (hopefully) the description in the Idea-section at spherical space form. Right now it reads as follows:

    A spherical space form is a quotient space S n/GS^n/G of a round Riemannian n-sphere (n2n \geq 2) by a subgroup GG of its isometry group, which acts freely and properly discontinuously.

    Equivalently, a spherical space form is a Riemannian manifold of constant positive sectional curvature (an elliptic geometry) which is connected and geodesically complete (see e.g. Gadhia 07, Lemma 5).

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 25th 2018
    • (edited Apr 25th 2018)

    finally spelled out the full statement (here) of the ADE-classification of 7d spherical space forms equipped with spin structures admitting N4N \geq 4 Killing spinors

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 25th 2018

    Is the expectation that all of those 7d spherical space forms partake in the AdS4/CFT3-correspondence? That ABJM theory just concerns the A-type singularities?

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeApr 25th 2018
    • (edited Apr 25th 2018)

    Yes, that was the motivation for the classification by Figueroa-O’Farrill et al., stated in the first paragraphs of their MFFME 09 and MFFGME 09.

    The N=5N = 5-analogs of the ABJM model (hence for the dihedral and exceptional finite groups acting diagonally on 2 8\mathbb{H}^2 \simeq \mathbb{R}^8) have been identified (I have added pointers here).

    I am not sure about the state of the discussion of the N=4N =4-case. But clearly one expects this to exist.

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 25th 2018

    Thanks!

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeApr 25th 2018

    ah, the N=4N=4-case is discussed in section 4.3 of Bagger-Lambert-Mukhi-Papageorgakis 13. I am not sure, though, whether corresponding singularity structure is discussed

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