Subject: Re: question and job From: Jim Lin Date: Wed, 02 Mar 2005 07:54:41 -0800 To: Don Davis > hi, this is Jim Lin. This is a brief answer to Martin's question: > You can factor x Sq1 x thru secondary and primary operations if x cup x is zero. Look at the two stage postnikov system obtained by killing off the cup product square of a 2r class. It's associated to the secondary operation associated to Sq ^1 Sq ^2r. In the total space there will be an element v with reduced coproduct x tensor x. (it behaves like the divided power of x). It restricts to the fibre to be Sq1 of the 4r-1 fundamental class. Then Sq ^1 of v has the same coproduct of as x Sq ^1 x. Further, Sq 1 of v restricts to zero in the fibre, since Sq 1 Sq 1 is zero. Hence Sq 1 v - x Sq 1 x is a primitive that restricts to zero in the fibre, so it must come from the base ( by the Serre exact sequence). So it is some primary operation on the fundamental class in degree 2r.