Unstable homotopy invariance for finite fields

Unstable Homotopy Invariance and the Homology of Sl 2 (zt])

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...

Obstructions to Homotopy Invariance

2 7 M ar 1 99 8 Amalgamated Free Products , Unstable Homotopy Invariance

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(...

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(...

Homotopy invariance of higher signatures

We prove that the higher signature for any close oriented manifold is a homotopy invariant. 2000 MR Subject Classification 57N70, 57R95, 57R40