2 7 M ar 1 99 8 Amalgamated Free Products , Unstable Homotopy Invariance
نویسنده
چکیده
We prove that if R is a domain with many units, then the natural inclusion E2(R) → E2(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 E2(Z[t]) and show that a great deal of the homology of E2(Z[t]) maps nontrivially into the homology of SL2(Z[t]). As a consequence, we show that the latter is not finitely generated in all positive degrees.
منابع مشابه
Amalgamated Free Products, Unstable Homotopy Invariance, and the Homology of SL2(Z[t])
We prove that if R is a domain with many units, then the natural inclusion E2(R) → E2(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 E2(Z[t]) and show that a great deal of the homology of E2(Z[t]) maps nontrivially into the homology of SL2(...
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We prove that if R is a domain with many units, then the natural inclusion E 2 (R) ! E 2 (Rt]) induces an isomorphism in integral homology. This is a consequence of the existence of an amalgamated free product decomposition of E 2 (Rt]). We also use this decomposition to study the homology of E 2 (Zt]) and show that a great deal of the homology of E 2 (Zt]) maps nontrivially into the homology o...
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