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Gauss-Bonnet theorem in the Hawking/Ellis book
At the page 336 of Hawking, Ellis: The Large Scale Structure of Space-Time, the Gauss-Bonnet theorem is stated as
$$\int_H \hat{R}\ d\hat{S} = 2\pi \chi(H) \qquad (1)$$
with
$$\hat{R} = R_{abcd} ...
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gauss-bonnet gravity constraints from string theory
recently there has been advances in observational constraints of gravity theories that contains scalars coupled to the gauss-bonnet topological term:
http://arxiv.org/abs/0704.0175
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