Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: CW-pair

Bottom of Page

1 to 8 of 8

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 24th 2016

    I gave CW-pair its own entry.

    • CommentRowNumber2.
    • CommentAuthorR.Arthur
    • CommentTimeNov 23rd 2021

    Remove Hatcher’s dead-link and add correct and live one.

    diff, v3, current

    • CommentRowNumber3.
    • CommentAuthorR.Arthur
    • CommentTimeNov 23rd 2021

    Changed array-diagram to tikz-cd.

    diff, v3, current

    • CommentRowNumber4.
    • CommentAuthorR.Arthur
    • CommentTimeNov 23rd 2021

    Remove redundant centering

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorR.Arthur
    • CommentTimeNov 23rd 2021

    Remove redundant centering

    diff, v3, current

    • CommentRowNumber6.
    • CommentAuthorR.Arthur
    • CommentTimeNov 23rd 2021
    Okay, took me a while to fix all the little nasty "bugs" I caused, but the page should be 'better' now. (At least with a working link and tikz-cd commuting diagrams).
    I will make sure that every time during my research I come across a nLab page with array commuting diagrams, I fix that page to have tikz-cd commuting diagrams. Likewise for broken Hatcher links.
    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 24th 2021

    Thanks!

    I will make sure that every time during my research I come across a nLab page with array commuting diagrams, I fix that page to have tikz-cd commuting diagrams.

    That sounds great. Will be much appreciated!

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJan 21st 2025
    • (edited Jan 21st 2025)

    added (here) the statement that collapsing contractible subcomplexes does not change the homotopy type, with pointer to Hatcher’s p. 11 and including the graphics for one of the examples Hatcher gives.

    Then added the following immediate generalization of this example:

    For Σ g,n 2\Sigma^2_{g,n} the result of equipping a closed surface Σ g 2\Sigma^2_g with n≥2n \geq 2 punctures, the one-point compactification (Σ g,n 2) *\big(\Sigma^2_{g,n}\big)^\ast is homotopy equivalent to the wedge sum of the original surface with n−1n-1 circles:

    (Σ g,n 2) *≃Σ g 2∨⋁ n−1S 1. \big(\Sigma^2_{g,n}\big)^\ast \;\simeq\; \Sigma^2_g \,\vee\, \textstyle{\bigvee_{n-1}} S^1 \,.

    diff, v4, current

1 to 8 of 8

  1.