Algebraic concordance order of almost classical knots.

Torsion in the concordance group of knots in S 3 can be studied with the algebraic concordance group . Here, is a field of characteristic χ () ≠ 2. The group was defined by Levine, who also obtained an algebraic classification when = ℚ. While the concordance group is abelian, it embeds into the non-abelian virtual knot concordance group . It is unknown if admits non-classical finite torsion. Here, we define the virtual algebraic concordance group for Seifert surfaces of almost classical knots. This is an analogue of for homologically trivial knots in thickened surfaces Σ × [ 0 , 1 ] , where Σ is closed and oriented. The main result is an algebraic classification of . A consequence of the classification is that ℚ embeds into ℚ and ℚ contains many nontrivial finite-order elements that are not algebraically concordant to any classical Seifert matrix. For = ℤ / 2 ℤ , we give a generalization of the Arf invariant. [ABSTRACT FROM AUTHOR]