Fundamental Groups of Commuting Elements in Lie Groups

Fundamental Groups of Commuting Elements in Lie Groups

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 computation of the mod-2 cohomology of the components of these spaces is also obtained.

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Hauptverfasser: Torres-Giese, Enrique, Sjerve, Denis
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Algebraic Topology
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Zusammenfassung: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 computation of the mod-2 cohomology of the components of these spaces is also obtained.
DOI:10.48550/arxiv.math/0609375