New knot invariants from instanton homology.
problem Bounding knot genus and double points.
method Instanton homology groups with local coefficients.
result 1-parameter family of homomorphisms from knot concordance group to reals.
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48 results for “concordance invariance”
New knot concordance invariants derived from regions in the plane.
problem Knot concordance and distinguishing knots from thin or algebraic ones.
method Associate invariants to regions in the plane, compute for specific knots, and use to obstruct concordances.
result Compute and use new invariants to obstruct concordances to specific types of knots.
New invariants from Heegaard Floer homology for knot concordance.
problem Understanding knot concordance.
method Truncated Heegaard Floer homology.
result Construction of new concordance invariants .
New knot concordance invariants from sl(n) cohomology.
problem Developing new invariants to distinguish knots.
method Construct piecewise linear maps from [0,1] to R, derived from sl(n) knot cohomology.
result Verify properties analogous to Upsilon invariant and define new concordance invariants.
Functorial properties of knot invariants under specific concordances.
problem Computing obstructions to regular Lagrangian concordances.
method Functoriality of EH class and LOSS invariant under Lagrangian concordances in Weinstein cobordisms.
result Computable obstructions to regular Lagrangian concordances.
Study algebraic concordance groups for non-trivial links.
problem Invariance of signature, Fox-Milnor condition, and Blanchfield pairing under concordance.
method Defined algebraic concordance groups using generalized Seifert matrices.
result Recovery of invariance of signature, Fox-Milnor condition, and Blanchfield pairing for concordant links.
Proves non-solvability of concordance groups using Milnor invariants.
problem Non-solvability of concordance groups of 2-string links and strongly invertible knots.
method Using Milnor invariants to prove non-solvability.
result Proves non-solvability of and equivariant concordance groups of strongly invertible knots.
Study of concordances between links in 4-space, defining new invariants.
problem Investigate the set of all embedded concordances between two fixed links in 4-space.
method Define Milnor-type invariants of the set of concordances, modulo indeterminacy.
result For slice links, these invariants classify the set of concordances up to link-homotopy.
New concordance invariants phi and phi_j are defined and studied.
problem Understanding the relationships between different concordance invariants.
method Defined and analyzed new invariants phi and phi_j, and provided recursive formulas.
result Found infinitely many knots with specific combinations of zero and nonzero phi invariant.
Study shows how concordance surgery impacts a 4D knot invariant.
problem Understanding how concordance surgery affects a specific 4D knot invariant.
method Used sutured Floer TQFT and a perturbed version of sutured Floer homology.
result Formula involving the graded Lefschetz number of the concordance map on knot Floer homology.
New concordance invariant from spectral sequence on Khovanov homology.
problem Concordance invariants from spectral sequences.
method Constructing from spectral sequence on Khovanov homology.
result Provides a bound on the nonorientable slice genus.
Extends knot concordance invariant to balanced spatial graphs using grid homology.
problem Defining a concordance invariant for balanced spatial graphs.
method Using grid homology to extend the invariant from knots to spatial graphs.
result The combinatorial invariant is a concordance invariant for balanced spatial graphs.
New link concordance invariants from perturbed sl(n) homology give lower bounds on slice genus and splitting number.
problem Link concordance and slice genus determination.
method Defining a family of invariants from perturbed sl(n) homology.
result Computes slice genus of positive links and determines splitting number of positive torus links.
New knots found with zero Upsilon but nonzero epsilon.
problem Finding knots with specific concordance invariants.
method Constructing new knots with linear independence in the smooth concordance group.
result Found knots with vanishing Upsilon but nonzero epsilon.
The study defines and explores almost-concordance classes of knots in 3-manifolds.
problem Defining and exploring almost-concordance classes of knots in 3-manifolds.
method Action of the concordance group of knots in the three-sphere on concordances of knots in arbitrary 3-manifolds; definition of almost-concordance; use of modified tau-invariant to obstruct almost-concordances.
result Existence of non-trivial almost-concordance classes in all non-abelian 3-manifolds; infinitely many nullhomologous non almost-concordant knots in L(p,1).
Study links' concordance using signatures and nullity.
problem Link concordance invariance of Levine-Tristram signatures.
method Determine invariance for complex numbers on the unit circle.
result Signature and nullity give link concordance invariants.
New knot concordance invariants from cyclic covers of prime power.
problem Constructing new knot concordance invariants.
method Considering m-fold cyclic branched covers with m a prime power.
result Computations of new invariants for some families of knots.
Link concordance and Whitney towers linked to Milnor invariants.
problem Link concordance and Whitney towers classification.
method Clasper surgeries, Whitney towers, and Milnor invariants.
result Link concordance and Whitney towers classified in terms of Milnor invariants.
New knot invariants bound genus and concordance genus.
problem Bounding knot genus and concordance genus.
method Defining secondary Upsilon invariants as piecewise linear functions.
result Secondary invariants detect knots not detected by Upsilon.
Study on 2-bridge knots, proving equivariant concordance order is infinite.
problem Equivariant concordance of 2-bridge knots.
method Formula for butterfly polynomial, two proofs of non-equivariant sliceness, new invariant for strongly invertible knots.
result Equivariant concordance order of 2-bridge knots is infinite.
Defines knot concordance invariant using instanton homology and Donaldson invariants.
problem Knot concordance and its classification.
method Defines an invariant for knots in the 3-sphere using Donaldson invariants and Floer's instanton homology.
result The invariant coincides with a special case of an invariant defined by Froyshov.
Knots and links in 3-manifolds are studied by applying intersection invariants to singular concordances. The resulting link invariants generalize the Arf invariant, the mod 2 Sato-Levine invariants, and Milnor's triple linking numbers. Besides fitting into a general theory of Whitney towers, these invariants provide ob…
We investigate the concordance properties of `parallel links' P(K), given by the (2,0) cable of a knot K. We focus on the question: if P(K) is concordant to a split link, is K necessarily slice? We show that if P(K) is smoothly concordant to a split link, then many smooth concordance invariants of K must vanish, includ…
New family of knots with epsilon invariant nonzero despite Upsilon and phi being zero.
problem Comparing smooth concordance invariants.
method Building an infinite family of knots.
result Found knots with epsilon invariant nonzero but Upsilon and phi zero.
New knot concordance invariants from instantons and Floer theory.
problem Defining and computing concordance invariants of knots.
method Equivariant singular instanton Floer theory with Chern-Simons filtration.
result Computing -invariant and fractional ideal invariants for two-bridge knots.
New invariants for link concordance defined using Whitehead doubles.
problem Defining and analyzing new concordance invariants for links.
method Extending slice-torus invariants to links, proving properties, and using Whitehead doubles.
result New strong concordance invariants for links, independent of slice-torus link invariants.
New invariant defined for unoriented knots, proving no factorization through topological concordance.
problem Defining and proving properties of unoriented slice-torus invariants.
method Introducing and proving properties of unoriented slice-torus invariants.
result Unoriented slice-torus invariants do not factor through the topological concordance group.
Formula derived for cabled knots' concordance invariants.
problem Understanding involutive concordance invariants of cabled knots.
method Proved a formula relating cabled knots' invariants to companion and pattern knots.
result Iterated cables of certain knots are not smoothly slice.
We study the eta-invariants of links and show that in many cases they form link concordance invariants, in particular that many eta-invariants vanish for slice links. This result contains and generalizes previous invariants by Smolinsky and Cha--Ko. We give a formula for the eta-invariant for boundary links. In several…
Paper gives a full-twist inequality for a knot concordance invariant ν^+.
problem Understanding the behavior of the ν^+ invariant under knot cobordisms.
method Developed a full-twist inequality for the ν^+ invariant and extended Wu's cabling formula.
result Extended Wu's cabling formula to all cables and introduced a partial order on ν^+ equivalence classes.
Smooth figure-eight knot cables have infinite order.
problem Proving infinite order of figure-eight knot cables.
method Introduced new concordance invariants via branched covers and real Seiberg-Witten Floer K-theory.
result Uniform proof for all -cables of the figure-eight knot.
This paper is a generalization of the author's previous work on link homotopy to link concordance. We show that the only real-valued finite type link concordance invariants are the linking numbers of the components.
The paper describes and analyzes a knot concordance invariant ε using grid homology.
problem Understanding and computing the knot concordance invariant ε.
method Combinatorial description and grid homology techniques.
result Computed values and properties of the invariant ε for specific knots.
Study shows concordance invariants bound Turaev genus.
problem Understanding the Turaev genus of knots.
method Using differences between concordance invariants, including Rasmussen's -invariant and -invariants.
result Established lower bounds for Turaev genus and provided examples of quasi-alternating knots with specific genus values.
2-knots with symmetry are classified up to equivariant concordance.
problem Classifying 2-knots with symmetry up to equivariant concordance.
method Constructing a new invariant called periodic, based on the Arf invariant.
result The smooth equivariant concordance group of 2-knots in is isomorphic to for all .
Study shows knots with coprime polynomials can't be concordant.
problem Primary decomposition of knot concordance.
method Using von Neumann rho-invariants and solvable filtration.
result Nonnegative integer n-solvable knots with coprime polynomials are not concordant.
0-Concordance of 2-knotsmath.GT
The paper shows infinitely many types of 2-knots in 4-space.
problem Understanding the equivalence of 2-knots in 4-dimensional space.
method Using Rochlin's invariant and Heegaard-Floer homology.
result There are infinitely many 0-concordance classes of 2-knots.
Combining known spectral sequences with a new spectral sequence relating reduced and unreduced sl(N)-homology yields a relationship between the Homflypt-homology of a knot and its sl(N)-concordance invariants. As an application, some of the sl(N)-concordance invariants are shown to be linearly independent.
Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complexmath.GT
Study annular concordance invariants and refine transverse link invariants.
problem Understanding annular concordance and transverse links.
method Defined and studied annular concordance invariant, introduced modified chain complex, and refined transverse invariant.
result Refined transverse invariant and studied its relationship with transverse and braid monodromy properties.
The concordance genus of a knot K is the minimum three-genus among all knots concordant to K. For prime knots of 10 or fewer crossings there have been three knots for which the concordance genus was unknown. Those three cases are now resolved. Two of the cases are settled using invariants of Levine's algebraic concorda…
Study calculates special knot properties for specific types of knots.
problem Computing involutive concordance invariants for (1,1)-knots.
method Computed involutive concordance invariants for 10- and 11-crossing (1,1)-knots.
result Computed involutive concordance invariants for specific (1,1)-knots.
We give necessary conditions of a surface-knot to be ribbon concordant to another, by introducing a new variant of the cocycle invariant of surface-knots in addition to using the invariant already known. We demonstrate that twist-spins of some torus knots are not ribbon concordant to their orientation reversed images.
We show that the twisted signature invariants of boundary link concordance derived from unitary representations of the free group are actually ordinary link concordance invariants. We also show how the discontinuity locus of this signature function is determined by Seifert matrices of the link.
New obstructions show links with vanishing Milnor invariants may not be concordant to homology boundary links.
problem Understanding links with vanishing Milnor invariants and their concordance properties.
method Developing new obstructions and examples within the solvable filtration framework.
result Existence of links with vanishing Milnor invariants that are not concordant to homology boundary links.
Bennequin-Plamenevskaya-Shumakovitch type inequalities for Kronheimer-Mrowka's concordance invariantmath.GT
Lower bounds for a knot invariant are derived using computations and cobordism inequality.
problem Calculating the concordance invariant for knots.
method Computation for torus knots, cobordism inequality of , and arguments for slice-torus invariants.
result Lower bounds for are derived for knots.
Study shows infinite families of knots with same Seifert form, not concordant to others.
problem Understanding knots with the same Seifert form and their concordance properties.
method Used Cheeger-Gromov-von Neumann rho-invariants and polynomial splittings of metabelian rho-invariants.
result Found infinite families of knots with the same Seifert form that are not concordant to others.
The paper defines and studies new types of links in 4-manifolds.
problem Understanding and classifying links in 4-dimensional spaces.
method Defining and studying r-shake slice and r-shake concordant links, providing examples and characterizations.
result Characterizations of shake slice and shake concordant links for r=0, and proving invariants of shake concordance.
Ozsvath-Stipsicz-Szabo recently defined a one-parameter family, upsilon of K at t, of concordance invariants associated to the knot Floer complex. We compare their invariant to the {-1, 0, 1}-valued concordance invariant epsilon, which is also associated to the knot Floer complex. In particular, we give an example of a…