A minimal set of generators for the cohomology is:
w
2
(r
4
) of degree 2
w
1
(r
2
) of degree 1
w
1
(r
4
) of degree 1
The Steenrod operations are as follows:
Sq
1
(w
2
(r
4
)) = w
2
(r
4
)w
1
(r
4
)
Here is a minimal system of equations:
(1) w
1
(r
2
)
2
+ w
1
(r
2
)w
1
(r
4
) = 0
Stiefel-Whitney classes:
w
1
(r
1
) = w
1
(r
2
) + w
1
(r
4
)
w
1
(r
2
) = w
1
(r
2
)
w
1
(r
3
) = w
1
(r
4
)
w
1
(r
4
) = w
1
(r
4
)
w
2
(r
4
) = w
2
(r
4
)
Chern classes:
c
1
(r
1
) = w
1
(r
2
)
2
+ w
1
(r
4
)
2
c
1
(r
2
) = w
1
(r
2
)
2
c
1
(r
3
) = w
1
(r
4
)
2
c
1
(r
4
) = w
1
(r
4
)
2
c
2
(r
4
) = w
2
(r
4
)
2
The algebra of Milnor constants is generated by:
c
2
(r
4
)
c
1
(r
2
)
c
1
(r
1
) + c
1
(r
2
)
Note: the only algebraic cycles in the cohomology are Chern classes.
The results above have been produced during the second run in April, 2008.