Homology of SLn and GLn over an infinite field
Behrooz Mirzaii
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).
Create a lesson
Related papers
Geometric K-homology and operator K-theory for Hilbert manifolds
Doman Takata
Mixed Tate motives over number fields
Alexander Kupers, Daniil Rudenko, Ismael Sierra
The integral homology of SL2(Z[1/n])
Isadora Vanzella Picinini, Behrooz Mirzaii
Finite-coefficient K-theory of henselian valued fields and Gersten injectivity
Niels Feld
Deformations and homotopy theory of Rota-Baxter Lie algebras
Jun Chen, Kai Wang, Guodong Zhou
On the abelianization of congruence subgroups of SL2 over S-integers
Pedro H. Amorim, Isadora V. Picinini, Bruno R. Ramos et al.