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I am reading algebraic topology by Artin, and he gives the following definition. Let $X$ be a topological space. We define a homomorphism $sd_X: S_p(X) \to S_p(X)$ by induction. If $T: \Delta_0 \to X$ is a singular 0-simplex, we define $sd_XT = T$. Now suppose $sd_X$ is defined in dimensions less than $p$. If $i_p: \Delta_p \to \Delta_p$ is the identity map, let $\hat{\Delta}_p$ denote the barycenter of $\Delta_p$ and define $sd_{\Delta_p}i_p = (-1)^p[sd_{\Delta_p}(\partial i_p), \hat{\Delta}_p]$. Then define $sd_XT = T_\#(sd_{\Delta_p} i_p)$.

I've tried for probably 10 hours to compute $sdΔ1(∂i_1)(1/4,1/4)$ and can not. I have no clue how to start.

user68330
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  • People keep tagging this as a duplicate and it clearly is not. Please do not erase this. – user68330 Mar 25 '13 at 02:15
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    What question do people think it is a duplicate of? – Potato Mar 25 '13 at 02:28
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    http://math.stackexchange.com/questions/339295/algebraic-topology-artin?rq=1 this maybe? – Alex J Best Mar 25 '13 at 02:32
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    Why are you creating 20,000 proxy accounts? – Alex Youcis Mar 25 '13 at 02:33
  • What is a proxy account? I never made an account. – user68330 Mar 25 '13 at 02:40
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    To be fair, I don't think s/he understands that this is posted under a new account. – Potato Mar 25 '13 at 02:46
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    I am legitimately having a hard time understanding the question posted. I know it may be very easy but I am having a hard time grasping what the definition means. Not trying to pull anything on anyone. I don't know what a gravatar is. I just pick a name and email and it lets me post. – user68330 Mar 25 '13 at 02:54
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    No, it's not a very easy question. And even if it were, that's not a problem. You might want to register an account, and ask to have your posts merged (after all, you have gained reputation already, and it is nice to have one place to keep all your questions/answers together so that you can go back and reference them.) If/when you do register for an account (or if you can remember your log-in user/password from when you posted previously), you can click on the "flag" link and request that a moderator merge your accounts. – amWhy Mar 25 '13 at 03:04
  • You should create a named account and have all your questions merged. – Potato Mar 25 '13 at 03:19
  • Also, is this in the context of a proof? I recommend looking for the equivalent material in Hatcher (available free online). – Potato Mar 25 '13 at 03:20
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    (Also, the poster seems to be right that the last time s/he posted this question, it was unfairly closed as a duplicate. See http://math.stackexchange.com/questions/339772/a-question-on-algebraic-topology ) – Potato Mar 25 '13 at 03:22
  • Don't know if I would recommend looking for this in Hatcher (I don't have it in front of me but I would guess it's probably buried in the proof of excision). But if you can get your hands on Tammo tom Dieck's book, I think it's in section 9.4 if I recall correctly. –  Mar 25 '13 at 03:39

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