Twisted cohomology pairings of knots III; triple cup products
Takefumi Nosaka
TL;DR
This paper introduces a topological invariant called a trilinear form for links, relating it to twisted triple cup products and providing computational examples, especially for hyperbolic links and certain knots.
Contribution
It establishes a new topological invariant based on twisted cohomology pairings and relates it to triple cup products for specific classes of links.
Findings
The trilinear form equals the pairing of the twisted triple cup product and the fundamental relative 3-class for hyperbolic links and certain knots.
Provides explicit examples of computing the new invariant.
Connects the invariant to known topological structures in knot theory.
Abstract
Given a representation of a link group, we introduce a trilinear form, as a topological invariant. We show that, if the link is either hyperbolic or a knot with malnormality, then the trilinear form equals the pairing of the (twisted) triple cup product and the fundamental relative 3-class. Further, we give some examples of the computation.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics