Abstract
The present work continues earlier investigations by DuPont, Parry and this writer. One of our motivating problems is the Scissors Congruence Problem (or Extended Third Problem of Hilbert). In 3-dimensional hyperbolic and spherical spaces, this problem has a close relation with the Quillen algebraic Ks-group of iF where [F denotes one of the three classical real division algebras R, C or IH. This relation arises by way of the third integral Eilenberg-MacLane homology group of the classical group SL(2, [F), homology stabilization theorems and the theorem of Hurewicz. The principal results are summarized below. Let D be one of the three real division algebras or any infinite field F with Fx=(Fx)6. In simplified form, we have
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