We investigate the mapping class groups of diffeomorphisms fixing a frame at a point for general classes of 3-manifolds. These groups form the equivalent to the groups of large gauge transformations in Yang-Mills theories. They are also isomorphic to the fundamental groups of the spaces of 3-metrics modulo diffeomorphisms, which are the analogues in General Relativity to gauge-orbit spaces in gauge theories.
@article{bwmeta1.element.bwnjournal-article-bcpv39z1p303bwm, author = {Giulini, Domenico}, title = {The Group of Large Diffeomorphisms in General Relativity}, journal = {Banach Center Publications}, volume = {38}, year = {1997}, pages = {303-315}, zbl = {0881.57031}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv39z1p303bwm} }
Giulini, Domenico. The Group of Large Diffeomorphisms in General Relativity. Banach Center Publications, Tome 38 (1997) pp. 303-315. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv39z1p303bwm/
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