Homology of SL_n and GL_n over an infinite field

Details Homology of SL_n and GL_n over an infinite field Homology of SL_n and GL_n over an infinite field

2006-05-29

arxiv.org/abs/math/0605722v1

published as `Homology of GLn: injectivity conjecture for GL4.' Math Ann. 304 (2008), no.1, 159-184

Mathematics

K-Theory and Homology

26 pages, Latex

Scientific paper

The homology of GL_n(F) and SL_n(F) is studied, where F is an infinite field. Our main theorem states that the natural map H_4(GL_3(F), k) --> H_4(GL_4(F), k) is injective where k is a field with char(k) \neq 2, 3. For algebraically closed field F, we prove a better result, namely, H_4(GL_3(F), Z) --> H_4(GL_4(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 K_4(F).

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