Some mildly wild circles in Sn arising from algebraic K-Theory

We study wild embeddings of S¹ in Sⁿ which are tame in a sense introduced by Quinn. We show that if is a finitely presented group with H₁()=H₂()=0, then any finiteness obstruction K₀() can be realized on the complement of such an embedded S¹. We also realize trivially symmetric K_–1() obstructions on the complements of such embeddings. For trivially symmetric , the embeddings constructed are shown to be isotopy homogeneous.