Order 2 Algebraically Slice Knots
نویسنده
چکیده
The concordance group of algebraically slice knots is the subgroup of the classical knot concordance group formed by algebraically slice knots. Results of Casson and Gordon and of Jiang showed that this group contains in infinitely generated free (abelian) subgroup. Here it is shown that the concordance group of algebraically slice knots also contain elements of finite order; in fact it contains an infinite subgroup generated by elements of order 2. AMS Classification 57M25; 57N70, 57Q20
منابع مشابه
Infinite Order Amphicheiral Knots
In 1977 Gordon [G] asked whether every class of order two in the classical knot concordance group can be represented by an amphicheiral knot. The question remains open although counterexamples in higher dimensions are now known to exist [CM]. This problem is more naturally stated in terms of negative amphicheiral knots, since such knots represent 2–torsion in concordance; that is, if K is negat...
متن کامل05 9 v 1 [ m at h . G T ] 1 3 A ug 1 99 8 Order 2 Algebraically Slice Knots
The classical knot concordance group, C, was defined by Fox [F] in 1962. The work of Fox and Milnor [FM], along with that of Murasugi [M] and Levine [Le1, Le2], revealed fundamental aspects of the structure of C. Since then there has been tremendous progress in 3and 4-dimensional geometric topology, yet nothing more is now known about the underlying group structure of C than was known in 1969. ...
متن کاملPretzel knots.dvi
We calculate the Ozsváth-Szabó τ concordance invariant of the pretzel knots P (2a+1, 2b+1, 2c+1) for any a, b, c ∈ Z. As an application we re-prove a result first obtained by Fintushel and Stern by which the only pretzel knot with Alexander polynomial 1 which is smoothly slice is the unknot. We also show that most pretzel knots which are algebraically slice are not smoothly slice. A further app...
متن کاملA Second Order Algebraic Knot Concordance Group
Let Knots be the abelian monoid of isotopy classes of knots S ⊂ S under connected sum, and let C be the topological knot concordance group of knots modulo slice knots. Cochran-OrrTeichner [COT03] defined a filtration of C: C ⊃ F(0) ⊃ F(0.5) ⊃ F(1) ⊃ F(1.5) ⊃ F(2) ⊃ . . . The quotient C/F(0.5) is isomorphic to Levine’s algebraic concordance group AC1 [Lev69]; F(0.5) is the algebraically slice kn...
متن کاملNew Obstructions to Doubly Slicing Knots
A knot in the 3-sphere is called doubly slice if it is a slice of an unknotted 2-sphere in the 4-sphere. We give a bi-sequence of new obstructions for a knot being doubly slice. We construct it following the idea of Cochran-Orr-Teichner’s filtration of the classical knot concordance group. This yields a bi-filtration of the monoid of knots (under the connected sum operation) indexed by pairs of...
متن کامل