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Mar 7, 2013 at 17:20 comment added Markus Land So this canonical map $MU \to MO$ will surely factor over $MSO$, right? Can one describe what formal group law it classifies? Do you know any references where this map is studied?
Feb 17, 2011 at 12:28 history edited Neil Strickland CC BY-SA 2.5
Added answer to follow-up question
Feb 17, 2011 at 10:39 comment added Neil Strickland As $F$ is a wedge of $H/2$'s, the same is true of $F\wedge F$, so the multiplication map $F\wedge F\to F$ decomposes into maps $H/2\to H/2$ (of various degrees) ie Steenrod operations. Thus, the ring structure is determined by the Steenrod module structure of the mod 2 homology, but it may package the information in a more convenient way.
Feb 17, 2011 at 9:15 comment added Oscar Randal-Williams Couldn't the ring structure on $F$ give you new information?
Feb 17, 2011 at 8:56 vote accept Mark Grant
Feb 16, 2011 at 10:12 history answered Neil Strickland CC BY-SA 2.5