Session D8 - Classical Gravitation.
ORAL session, Saturday afternoon, May 01
Governor's Square 17, Adam's Mark Hotel
Ashtekar and Samuel have shown that Bianchi cosmological models with compact spatial sections must be of Bianchi class A. Motivated by general results on the symmetry reduction of variational principles, we show how to extend the Ashtekar-Samuel results to the setting of weakly locally homogeneous spaces as defined, e.g., by Singer and Thurston. More precisely, it is shown that any m-dimensional homogeneous space G/K admitting a G-invariant volume form admits a compact discrete quotient only if the Lie algebra cohomology of G relative to K is non-vanishing at degree m.