Algebraic knots are algebraically dependent
نویسندگان
چکیده
منابع مشابه
Order 2 Algebraically Slice Knots
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 contain...
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Let F be an incompressible, meridionally incompressible and not boundary-parallel surface in the complement of an algebraic tangle (B, T ). Then F separates the strings of T in B and the boundary slope of F is uniquely determined by (B, T ) and hence we can define the slope of the algebraic tangle. In addition to the Conway’s tangle sum, we define a natural product of two tangles. The slopes an...
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In the first half, we’ll construct algebraic invariants and go over the classification of high dimensional simple knots. For reference, see Farber, Classification of simple knots. In the second half, we’ll compute invariants and discuss connections to number theory. Time permitting, we’ll go over applications of these invariants. In its most generality, knot theory studies the embeddings of man...
متن کاملSplitting the Concordance Group of Algebraically Slice Knots
As a corollary of work of Ozsváth and Szabó, it is shown that the classical concordance group of algebraically slice knots has an infinite cyclic summand and in particular is not a divisible group. Let A denote the concordance group of algebraically slice knots, the kernel of Levine’s homomorphism φ : C → G, where C is the classical knot concordance group and G is Levine’s algebraic concordance...
متن کاملRational Structure on Algebraic Tangles and Closed Incompressible Surfaces in the Complements of Algebraically Alternating Knots and Links
Let F be an incompressible, meridionally incompressible and not boundary-parallel surface with boundary in the complement of an algebraic tangle (B, T ). Then F separates the strings of T in B and the boundary slope of F is uniquely determined by (B, T ) and hence we can define the slope of the algebraic tangle. In addition to the Conway’s tangle sum, we define a natural product of two tangles....
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1983
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1983-0677257-5