Amalgamated free products, unstable homotopy invariance, and the homology of SL_2(Z[t])
| dc.creator | Knudson, Kevin P. | |
| dc.date | 1998-03-27 | |
| dc.date.accessioned | 2026-07-07T05:24:14Z | |
| dc.date.available | 2026-07-07T05:24:14Z | |
| dc.description | We show that if R is an integral domain with many units, then the inclusion E_2(R) --> E_2(R[t]) induces an isomorphism in integral homology. This is a consequence of the existence of an amalgamated free product decomposition for E_2(R[t]). We also use this decomposition to study the homology of E_2(Z[t]). We show that H_i(E_2(Z[t]),Z) contains a countable rank free summand for each i>0 and that this summand maps nontrivially into H_i(SL_2(Z[t]),Z); hence, the latter is not finitely generated. This improves on a result of Grunewald, et.al., which states that SL_2(Z[t]) has free quotients of countable rank (and hence, H_1(SL_2(Z[t]) is not finitely generated). | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/9803139 | |
| dc.identifier | http://arxiv.org/abs/math/9803139 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76756 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Group Theory | |
| dc.subject | 20G10; 19D50 | |
| dc.title | Amalgamated free products, unstable homotopy invariance, and the homology of SL_2(Z[t]) | |
| dc.type | text |