Difference between revisions of "User:Alec/Bitchin"
From Maths
(Silly) |
(Fleshed out) |
||
| (One intermediate revision by the same user not shown) | |||
| Line 1: | Line 1: | ||
| + | ==Dispute== | ||
| + | <div style="float:right;margin:0px;margin-left:0.2em"> | ||
{| class="wikitable" border="1" style="overflow:hidden;max-width:35em;" | {| class="wikitable" border="1" style="overflow:hidden;max-width:35em;" | ||
|- | |- | ||
| − | | <center><span style="font-size:1.2em;"><mm>\xymatrix{ & C_n(X) \ar[rr]^f \ar[d]_{\pi_1} \ar[dl]_{\pi_2} & & C_{n-1}(X) \ar[d]^{\pi_3} & \\ | + | | <center><span style="font-size:1.2em;"><mm>\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@{.>}@/^9.5ex/[urrr]^{f_2'} & \frac{C_n(X)}{C_n(A)} & & \frac{C_{n-1}(X)}{C_{n-1}(A)} & | + | \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)} & |
}</mm></span></center> | }</mm></span></center> | ||
|- | |- | ||
| − | ! | + | ! 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) | ||
Latest revision as of 22:23, 14 February 2017
Dispute
- f′:Cn(X)Cn(A)→Cn−1(X)Cn−1(A)
Specifically it is claimed that:
- Ker(π1)⊆Ker(f)
But I don't yet see how that helps. Alec (talk) 22:23, 14 February 2017 (UTC)
