Twisted signatures of fibered knots
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Date
2021
Publication Type
Journal Article
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Abstract
This paper concerns twisted signature invariants of knots and 3-manifolds. In the fibered case, we reduce the computation of these invariants to the study of the intersection form and monodromy on the twisted homology of the fiber surface. Along the way, we use rings of power series to obtain new interpretations of the twisted Milnor pairing introduced by Kirk and Livingston. This allows us to relate these pairings to twisted Blanchfield pairings. Finally, we study the resulting signature invariants, all of which are twisted generalizations of the Levine-Tristram signature.
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published
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21 (4)
Pages / Article No.
1973 - 2036
Publisher
Mathematical Sciences Publishers
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Subject
Knot; Fibered knot; twisted Alexander polynomial; Milnor pairing; Blanchfield pairing; Casson–Gordon invariants
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Funding
181199 - Low-dimensional topology with a view toward the fourth dimension and complex geometry (SNF)