A Calculation of Blanchfield Pairings of 3-Manifolds and Knots

Friedl, Stefan; Powell, Mark

doi:10.17323/1609-4514-2017-17-1-59-77

Cited by 30 publications

(30 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The adjoints of the two Blanchfield pairings above fit into the following diagram. We have verified that it is hermitian and nonsingular (see [FP15] for an alternative argument). Inspection of the essential properties that we have used in the argument yields the following potentially useful proposition, which was Proposition 1.4 in the introduction.…”

Section: Recovering the Classical Blanchfield Pairingmentioning

confidence: 57%

Twisted Blanchfield Pairings and Symmetric Chain Complexes

Powell

2016

Q J Math

Self Cite

View full text Add to dashboard Cite

We define the twisted Blanchfield pairing of a symmetric triad of chain complexes over a group ring Z[π], together with a unitary representation of π over an Ore domain with involution. We prove that the pairing is sesquilinear, and we prove that it is hermitian and nonsingular under certain extra conditions. A twisted Blanchfield pairing is then associated to a 3-manifold together with a decomposition of its boundary into two pieces and a unitary representation of its fundamental group.T H 1 (N ; Z) × T H 1 (N ; Z) → Q/Z.

show abstract

Section: Recovering the Classical Blanchfield Pairingmentioning

confidence: 57%

Twisted Blanchfield Pairings and Symmetric Chain Complexes

Powell

2016

Q J Math

Self Cite

View full text Add to dashboard Cite

show abstract

“…called the Blanchfield pairing. The pairing can be computed using a Seifert matrix of K as follows, for more details see [14,22,28].…”

Section: Sliceness Obstructions From Twisted Alexander Polynomialsmentioning

confidence: 99%

Branched covers bounding rational homology balls

Aceto

Meier

Miller

et al. 2021

Algebr. Geom. Topol.

View full text Add to dashboard Cite

show abstract

“…] → 0, and κ is the so-called Kronecker evaluation (see e.g. [FP17] for details regarding this definition). The involution • on Z[t ±1 ] is given by p(t) = p(t −1 ), and for a Z[t ±1 ]-module M , M denotes the module given by the same abelian group as M , and p(t) acting as p(t).…”

Section: Twisted Alexander Polynomialsmentioning

confidence: 99%

Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials

Friedl¹,

Kitayama²,

Lewark³

et al. 2021

Can. J. Math.-J. Can. Math.

Self Cite

View full text Add to dashboard Cite

We establish homotopy ribbon concordance obstructions coming from the Blanchfield form and Levine-Tristram signatures. Then, as an application of twisted Alexander polynomials, we show that for every knot K with nontrivial Alexander polynomial, there exists an infinite family of knots that are all concordant to K and have the same Blanchfield form as K, such that no pair of knots in that family is homotopy ribbon concordant.

show abstract

A Calculation of Blanchfield Pairings of 3-Manifolds and Knots

Abstract: We calculate Blanchfield pairings of 3-manifolds. In particular, we give a formula for the Blanchfield pairing of a fibred 3-manifold and we give a new proof that the Blanchfield pairing of a knot can be expressed in terms of a Seifert matrix.

Cited by 30 publications

References 8 publications

Twisted Blanchfield Pairings and Symmetric Chain Complexes

Twisted Blanchfield Pairings and Symmetric Chain Complexes

Branched covers bounding rational homology balls

Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials

Contact Info

Product

Resources

About