All Physics Faculty Publications

Document Type

Article

Journal/Book Title/Conference

Classical and Quantum Gravity

Volume

21

Issue

11

Publisher

Institute of Physics

Publication Date

2004

First Page

L73

Last Page

L78

DOI

10.1088/0264-9381/21/11/L02

Abstract

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. 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.

Comments

Originally published by the Institute of Physics. Publisher's PDF and HTML fulltext can be accessed through Classical and Quantum Gravity. Author post-print available online through arXiv.org.

http://iopscience.iop.org/0264-9381/21/11/L02