Timeline for Two H-space structures on S^3 and [X,S^3] different as groups for each: Explicit Example?
Current License: CC BY-SA 3.0
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| Mar 17, 2015 at 13:36 | answer | added | Jeff Strom | timeline score: 5 | |
| Mar 17, 2015 at 10:19 | comment | added | Mark Grant | If $X$ is a closed oriented $3$-manifold, then maps $X\to S^3$ are classified by their degree. Since the degree can be detected homologically, and since any multiplication $m:S^3\times S^3\to S^3$ must do the obvious thing on third homology, I think all the groups are isomorphic when $X$ is an oriented $3$-manifold. (I leave this comment in case anyone else was thinking of using Hopf's theorem.) | |
| Mar 16, 2015 at 23:30 | history | asked | user1437 | CC BY-SA 3.0 |