By a recent result of Livingston, it is known that if a knot has a prime power branched cyclic cover that is not a homology sphere, then there is an infinite family of non-concordant knots having the same Seifert form as the knot. In this paper, we extend this result to the full extent. We show that if the knot has non…
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8 results for “non-concordance”
If a knot K has Seifert matrix V_K and has a prime power cyclic branched cover that is not a homology sphere, then there is an infinite family of non-concordant knots having Seifert matrix V_K.
Links with nontrivial Alexander polynomial which are topologically concordant to the Hopf linkmath.GT
We give infinitely many -component links with unknotted components which are topologically concordant to the Hopf link, but not smoothly concordant to any -component link with trivial Alexander polynomial. Our examples are pairwise non-concordant.
An oriented link L in a 3-sphere S in complex 2-space is a C-boundary if it bounds a piece of algebraic curve in the 4-ball bounded by S. Using Kronheimer and Mrowka's proof of the Thom Conjecture, we construct many oriented knots which are not concordant to a C-boundary. We use the two-variable HOMFLY polynomial to gi…
We use topological surgery in dimension four to give sufficient conditions for the zero framed surgery manifold of a 3-component link to be homology cobordant to the 3-torus, which arises from zero framed surgery on the Borromean rings, via a topological homology cobordism preserving the homotopy classes of the meridia…
New hyperbolic knots with convex Upsilon invariants constructed.
problem Constructing knots with convex Upsilon invariants.
method Combinatorial method for -knots and connected sum operation.
result Infinitely many mutually non-concordant hyperbolic knots with convex Upsilon invariants.
Extended signatures help distinguish non-concordant links.
problem Distinguishing non-concordant links using signatures.
method Defined and studied an n-variable extension of the Levine-Tristram signature, proving it a concordance invariant on a dense subset of the torus.
result Found an infinite family of 3-component links not concordant to their mirror images, detectable only by the extended signature.
New surfaces in 3D manifolds are found that cannot be smoothly deformed into each other.
problem Finding surfaces in 3D manifolds that cannot be smoothly deformed into each other.
method Constructing infinite families of homotopic surfaces in closed genus- surfaces, showing they are not smoothly image-concordant.
result Closed surfaces with common framed dual sphere can be -injective but not smoothly image-concordant.