A minimal set of generators for the cohomology is:
w
1
(r
4
) of degree 1
w
1
(r
2
) of degree 1
w
4
(r
5
) of degree 4
The Steenrod operations are as follows:
Sq
1
(w
4
(r
5
)) = 0
Sq
2
(w
4
(r
5
)) = 0
Sq
3
(w
4
(r
5
)) = 0
Here is a minimal system of equations:
(1) w
1
(r
4
)w
1
(r
2
) + w
1
(r
2
)
2
= 0
(2) w
1
(r
4
)
3
= 0
Stiefel-Whitney classes:
w
1
(r
1
) = w
1
(r
4
) + w
1
(r
2
)
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
1
(r
4
)
2
w
4
(r
5
) = w
4
(r
5
)
w
4
(r
6
) = w
4
(r
5
)
Chern classes:
c
1
(r
1
) = w
1
(r
4
)
2
+ w
1
(r
4
)w
1
(r
2
)
c
1
(r
2
) = w
1
(r
4
)w
1
(r
2
)
c
1
(r
3
) = w
1
(r
4
)
2
c
1
(r
4
) = w
1
(r
4
)
2
c
2
(r
4
) = 0
c
2
(r
5
) = w
4
(r
5
)
c
2
(r
6
) = w
4
(r
5
)
The algebra of Milnor constants is generated by:
c
2
(r
5
)
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.