Twisted signatures of fibered knots
arXiv:2001.05675 · doi:10.2140/agt.2021.21.1973
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 generalisations of the Levine-Tristram signature.
arXiv comment49 pages. v2: minor changes following referee's suggestions. Accepted for publication in Algebr. Geom. Topol
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