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pro vyhledávání: '"Davis, Christopher W."'
A geometric interpretation of the vanishing of Milnor's higher order linking numbers remains an important open problem in the study of link concordance. In the 1990's, works of Cochran-Orr and Livingston exhibit a potential resolution to this problem
Externí odkaz:
http://arxiv.org/abs/2305.11268
Publikováno v:
In Tetrahedron 21 August 2024 163
We show that in a prime, closed, oriented 3-manifold M, equivalent knots are isotopic if and only if the orientation preserving mapping class group is trivial. In the case of irreducible, closed, oriented $3$-manifolds we show the more general fact t
Externí odkaz:
http://arxiv.org/abs/2007.05796
Autor:
Davis, Christopher W.
Any knot in $S^3$ may be reduced to a slice knot by crossing changes. Indeed, this slice knot can be taken to be the unknot. In this paper we study the question of when the same holds for knots in homology spheres. We show that a knot in a homology s
Externí odkaz:
http://arxiv.org/abs/1903.09225
In the 1950's Milnor defined a family of higher order invariants generalizing the linking number. Even the first of these new invariants, the triple linking number, has received and fruitful study since its inception. In the case that $L$ has vanishi
Externí odkaz:
http://arxiv.org/abs/1901.05430
Akademický článek
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Akademický článek
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Publikováno v:
Transactions of the American Mathematical Society, 374 no. 6, 4449-4479, 2021
We produce infinite families of knots $\{K^i\}_{i\geq 1}$ for which the set of cables $\{K^i_{p,1}\}_{i,p\geq 1}$ is linearly independent in the knot concordance group. We arrange that these examples lie arbitrarily deep in the solvable and bipolar f
Externí odkaz:
http://arxiv.org/abs/1806.06225
Autor:
Davis, Christopher W.
In 2016 Levine showed that there exists a knot in a homology 3-sphere which is not smoothly concordant to any knot in the 3-sphere where one allows concordances in any smooth homology cobordism. Whether the same is true if one allows topological conc
Externí odkaz:
http://arxiv.org/abs/1803.01086
Publikováno v:
Journal of the LMS (2)98 no. 1, 59-84, 2018
We establish a number of results about smooth and topological concordance of knots in $S^1\times S^2$. The winding number of a knot in $S^1\times S^2$ is defined to be its class in $H_1(S^1\times S^2;\mathbb{Z})\cong \mathbb{Z}$. We show that there i
Externí odkaz:
http://arxiv.org/abs/1707.04542