Holonomy invariants of links and nonabelian Reidemeister torsion

  • Calvin McPhail-Snyder

    University of California, Berkeley; and Duke University, Durham, USA
Holonomy invariants of links and nonabelian Reidemeister torsion cover
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Abstract

We show that the reduced SL2(C)\operatorname{SL}_2(\mathbb{C})-twisted Burau representation can be obtained from the quantum group Uq(sl2)\mathcal{U}_q(\mathfrak{sl}_2) for q=iq = i a fourth root of unity and that representations of Uq(sl2)\mathcal{U}_q(\mathfrak{sl}_2) satisfy a type of Schur–Weyl duality with the Burau representation. As a consequence, the SL2(C)\operatorname{SL}_2(\mathbb{C})-twisted Reidemeister torsion of links can be obtained as a quantum invariant. Our construction is closely related to the quantum holonomy invariant of Blanchet–Geer–Patureau-Mirand–Reshetikhin, and we interpret their invariant as a twisted Conway potential.

Cite this article

Calvin McPhail-Snyder, Holonomy invariants of links and nonabelian Reidemeister torsion. Quantum Topol. 13 (2022), no. 1, pp. 55–135

DOI 10.4171/QT/160