Homology of SL_n and GL_n over an infinite field
Abstract
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).
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- May 2006
- DOI:
- arXiv:
- arXiv:math/0605722
- Bibcode:
- 2006math......5722M
- Keywords:
-
- Mathematics - K-Theory and Homology;
- 19D55;
- 19D45
- E-Print:
- 26 pages, Latex