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nLab > Latest Changes: nilpotent topological space

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 17th 2019

    added pointer to

    • Luis Scoccola, Nilpotent Types and Fracture Squares in Homotopy Type Theory (arXiv:1903.03245)

    diff, v6, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 30th 2020

    added pointer to

    • Peter Hilton, Nilpotency in group theory and topology, Publicacions de la Secció de Matemàtiques Vol. 26, No. 3 (1982), pp. 47-78 (jstor:43741908)

    diff, v8, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 30th 2020

    added pointer to

    diff, v8, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeSep 15th 2020

    I have added the following under “Examples”:

    Directly from the definition we have that:

    and more generally

    As a special case of this

    and thus

    • every loop space is nilpotent

      (since all its connected components are homotopy equivalent to the unit component, which is a connected H-space).

    (See May-Ponto 12, p. 49 (77 of 542))

    diff, v10, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeSep 15th 2020

    also:

    diff, v10, current

1 to 5 of 5

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