Difference between revisions of "User:Alec/Bitchin"

Latest revision as of 22:23, 14 February 2017

Set up
$\xymatrix{ & C_n(X) \ar@{-->}[drr]^{\pi_3\circ f} \ar[rr]^f \ar[d]_{\pi_1} \ar[dl]_{\pi_2} & & C_{n-1}(X) \ar[d]^{\pi_3} & \\ \frac{C_n(X)}{\text{Ker}(f)} \ar@{-->}@/_4.5ex/[rrr]_{\pi_3\circ f_2'}\ar@{.>}@/^9.5ex/[urrr]^{f_2'} & \frac{C_n(X)}{C_n(A)} & & \frac{C_{n-1}(X)}{C_{n-1}(A)} & }$

If

$f$ is say

$\partial_n:C_n(X)\rightarrow C_{n-1}(Y)$ in a chain complex (found in this case in singular homology theory) it is claimed that for any topological subspace of

$X$ that

$f$ induces a map:

Specifically it is claimed that:

But I don't yet see how that helps. Alec (talk) 22:23, 14 February 2017 (UTC)

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+==Dispute==
+<div style="float:right;margin:0px;margin-left:0.2em">
 {| class="wikitable" border="1" style="overflow:hidden;max-width:35em;"
 |-
@@ Line 5: / Line 7: @@
 }</mm></span></center>
 |-
-! Here it is
+! Set up
 |}
+</div>If {{M|f}} is say {{M|\partial_n:C_n(X)\rightarrow C_{n-1}(Y)}} in a [[chain complex]] (found in this case in [[singular homology theory]]) it is claimed that for any [[topological subspace]] of {{M|X}} that {{M|f}} induces a [[map]]:
+* {{M|f':\frac{C_n(X)}{C_n(A)}\rightarrow\frac{C_{n-1}(X)}{C_{n-1}(A)} }}
+Specifically it is claimed that:
+* {{M|\text{Ker}(\pi_1)\subseteq \text{Ker}(f)}}
+But I don't yet see how that helps. [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 22:23, 14 February 2017 (UTC)