Homology of SLn and GLn over an infinite field
Abstract
The homology of GLn(F) and SLn(F) is studied, where F is an infinite field. Our main theorem states that the natural map H4(GL3(F), k) --> H4(GL4(F), k) is injective where k is a field with char(k) ≠ 2, 3. For algebraically closed field F, we prove a better result, namely, H4(GL3(F), Z) --> H4(GL4(F), Z) is injective. We will prove a similar result replacing GL by SL. This is used to investigate the indecomposable part of the K-group K4(F).
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