Abstract
AbstractLet K be an arbitrary infinite field. The cohomology group $$H^{2}(SL(2,K);H_2 SL(2,K))$$
H
2
(
S
L
(
2
,
K
)
;
H
2
S
L
(
2
,
K
)
)
contains the class of the universal central extension. When studying representations of fundamental groups of surfaces in SL(2, K) it is useful to have classes stable under deformations (Fenchel-Nielsen twists) of representations. We identify the maximal quotient of the universal class which is stable under twists as the Witt class of Nekovàř. The Milnor-Wood inequality asserts that an $$SL(2,\textbf{R})$$
S
L
(
2
,
R
)
-bundle over a surface of genus g admits a flat structure if and only if its Euler number is $$\le (g - 1)$$
≤
(
g
-
1
)
. We establish an analog of this inequality, and a saturation result for the Witt class. The result is sharp for the field of rationals, but not sharp in general.
Publisher
Springer Science and Business Media LLC