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Bulletin of the London Mathematical Society Advance Access originally published online on February 4, 2008
Bulletin of the London Mathematical Society 2008 40(1):65-76; doi:10.1112/blms/bdm094
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© 2008 London Mathematical Society

Fundamental groups of commuting elements in Lie groups

E. Torres Giese and D. Sjerve

Mathematics Department
University of British Columbia
Vancouver, BC
Canada
sjer@math.ubc.ca

Received 20 November 2006. Revision received 13 July 2007.

We compute the fundamental group of the spaces of ordered commuting n-tuples of elements in the Lie groups SU(2), U(2) and SO(3). For SO(3) the mod-2 cohomology of the components of these spaces is also obtained.

2000 Mathematics Subject Classification 55P99 (primary), 22E15 (secondary).

The first author is supported by a Conacyt fellowship. The second author is supported by NSERC Discovery grant A7218.


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