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Mar 31, 2020 at 14:11 comment added HJRW I'm not certain that this question is any easier than the Whitehead conjecture itself!
Mar 27, 2020 at 4:23 history edited user101010 CC BY-SA 4.0
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Mar 27, 2020 at 2:43 comment added mme For the final question: if $A \subset B$ is an inclusion of 2-complexes, then $H_2(A)$ injects into $H_2(B)$ (as $H_3(A,B) = 0$ for dimensions reasons). So for instance $S^2$ can't be null as a subcomplex of any 2-complex.
Mar 27, 2020 at 2:03 history asked user101010 CC BY-SA 4.0