Timeline for Maps which induce the same homomorphism on homotopy and homology groups are homotopic
Current License: CC BY-SA 3.0
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| Apr 7, 2015 at 21:16 | comment | added | Samarkand | James, thank you for your answer. I have read the definitions and it seems that phantom maps are $f:X\rightarrow Y$ such that restriction of $f$ to each skeleton is null-homotopic. So, this definition is of interest when $X$ is infinite dimensional. Is there some theory for finite complexes? For example, when $X$ and $Y$ are 2-dimensional, how can we check that map $f:X\rightarrow Y$ satisfy $0=f_*:\pi_2 X \rightarrow \pi_2 Y$. | |
| Feb 13, 2015 at 2:22 | history | edited | James Schwass | CC BY-SA 3.0 |
added references
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| Feb 13, 2015 at 1:21 | history | answered | James Schwass | CC BY-SA 3.0 |