Homology Stability for the Special Linear Group of a Field and Milnor-Witt -theory
Let be a field of characteristic zero and let be the stabilization homomorphism from the th integral homology of to the th integral homology of . We prove the following results: For all is an isomorphism if and is surjective for , confirming a conjecture of C-H. Sah. is an isomorphism when is odd and when is even the kernel is isomorphic to the st power of the fundamental ideal of the Witt Ring of . When is even the cokernel of is isomorphic to the th Milnor-Witt -theory group of . When is odd, the cokernel of is isomorphic to the square of the th Milnor -group of .