# R-Equivalence and 1-Connectedness in Anisotropic Groups

@article{Balwe2014REquivalenceA1,
title={R-Equivalence and 1-Connectedness in Anisotropic Groups},
author={Chetan T. Balwe and Anand Sawant},
journal={International Mathematics Research Notices},
year={2014},
volume={2015},
pages={11816-11827}
}
• Published 28 August 2014
• Mathematics
• International Mathematics Research Notices
We show that if G is an anisotropic, semisimple, absolutely almost simple, simply connected group over a field k, then two elements of G over any field extension of k are R-equivalent if and only if they are A^1-equivalent. As a consequence, we see that Sing_*(G) cannot be A^1-local for such groups. This implies that the A^1-connected components of a semisimple, absolutely almost simple, simply connected group over a field k form a sheaf of abelian groups.
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