Rank One Groups
The homology of rank one linear groups (SL2, PGL2) often can be computed via the action of the group on a suitable simplicial complex. There is the well-known tiling of the hyperbolic plane by SL2(ℤ)-translates of an ideal triangle (see, e.g. , p. 215) and there is the Bruhat-Tits tree associated to a field with discrete valuation. Often, the action implies something about the structure of the group such as the existence of an amalgamated free product decomposition.
KeywordsExact Sequence Elliptic Curve Spectral Sequence Fundamental Domain Integral Homology
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