Twisted Alexander polynomial of links in the projective space
Vu Q. Huynh, Thang T. Q. Le
TL;DR
This paper investigates a twisted Alexander polynomial for links in the projective space using Reidemeister torsion, deriving a skein relation for a normalized version of the polynomial.
Contribution
It introduces a new approach to study the twisted Alexander polynomial in projective space via sign-refined torsion and establishes a skein relation for it.
Findings
Derived a skein relation for the normalized twisted Alexander polynomial.
Applied Reidemeister torsion to links in the projective space.
Provided a new computational tool for link invariants in non-orientable 3-manifolds.
Abstract
We use Reidemeister torsion to study a twisted Alexander polynomial, as defined by Turaev, for links in the projective space. Using sign-refined torsion we derive a skein relation for a normalized form of this polynomial.
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Taxonomy
TopicsGeometric and Algebraic Topology · Organometallic Complex Synthesis and Catalysis · Bone health and treatments