Unstable homotopy invariance and the homology of SL2 (Z [t])
KP Knudson - Journal of Pure and Applied Algebra, 2000 - Elsevier
Journal of Pure and Applied Algebra, 2000•Elsevier
We prove that if R is a domain with many units, then the natural 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 of E2 (R [t]). We also use this decomposition to
study the homology of E 2 (Z [t]) and show that a great deal of the homology of E 2 (Z [t])
maps nontrivially into the homology of SL 2 (Z [t]). As a consequence, we show that the latter
is not finitely generated in all positive degrees.
induces an isomorphism in integral homology. This is a consequence of the existence of an
amalgamated free product decomposition of E2 (R [t]). We also use this decomposition to
study the homology of E 2 (Z [t]) and show that a great deal of the homology of E 2 (Z [t])
maps nontrivially into the homology of SL 2 (Z [t]). As a consequence, we show that the latter
is not finitely generated in all positive degrees.
We prove that if R is a domain with many units, then the natural 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 of E2(R[t]). We also use this decomposition to study the homology of E 2( Z [t]) and show that a great deal of the homology of E 2( Z [t]) maps nontrivially into the homology of SL 2( Z [t]) . As a consequence, we show that the latter is not finitely generated in all positive degrees.
Elsevier
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