Abstract
The relation between SO(1, 2 p − 1) Chern-Simons forms and SO(1, 2 p − 2) Gauss-Bonnet forms in 2 p − 1 dimensions is discussed in detail based on recent results by Chamseddine. This approach singles out a special linear combination of Gauss-Bonnet terms as a lagrangian for gravity in odd dimensions. We show that in eleven dimensions this theory naturally admits spontaneous compactification over the four-dimensional Minkowski space and in some sense even distinguishes four dimensions. Similar results are obtained in any odd dimension. We also find a certain degeneracy of the field equations which might cause a problem for such a “topological gauge theory of gravity”.
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