C G Torre 2004 Class. Quantum Grav. 21 L73 doi:10.1088/0264-9381/21/11/L02
C G Torre
Show affiliationsAshtekar 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. In particular, it is shown that any m-dimensional homogeneous space G/K admitting a G-invariant volume form will allow a compact discrete quotient only if the Lie algebra cohomology of G relative to K is non-vanishing at degree m.
04.60.Kz Lower dimensional models; minisuperspace models
02.20.Sv Lie algebras of Lie groups
04.20.Gz Spacetime topology, causal structure, spinor structure
22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
17B56 Cohomology of Lie (super)algebras
57T15 Homology and cohomology of homogeneous spaces of Lie groups
Issue 11 (7 June 2004)
Received 23 February 2004
Published 24 April 2004
C G Torre 2004 Class. Quantum Grav. 21 L73
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