Quantum relatives of the Alexander polynomial

DOI10.1090/S1061-0022-07-00956-9zbMath1149.57024arXivmath/0204290OpenAlexW2964096122MaRDI QIDQ5442118

O. Ya. Viro

Publication date: 15 February 2008

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0204290

zbMATH Keywords

Alexander polynomialquantum topologyquantum supergroupConway functioncolored framed trivalent graphsReshetikhin-Turaev functors

Mathematics Subject Classification ID

Related Items (26)

Categorification of tensor powers of the vector representation of \(U_q(\mathfrak{gl}(1| 1))\) ⋮ Holonomy invariants of links and nonabelian Reidemeister torsion ⋮ 𝔤𝔩(1|1)-Alexander polynomial for 3-manifolds ⋮ The differential graded odd nilHecke algebra ⋮ Non-semi-simple TQFTs, Reidemeister torsion and Kashaev's invariants ⋮ Khovanov-Seidel quiver algebras and Ozsváth-Szabó's bordered theory ⋮ An Alexander polynomial for MOY graphs ⋮ Multivariable link invariants arising from \(\mathfrak {sl}(2|1)\) and the Alexander polynomial ⋮ Seifert-Torres type formulas for the Alexander polynomial from quantum \(\mathfrak{sl}_2\) ⋮ Other quantum relatives of the Alexander polynomial through the Links-Gould invariants ⋮ Quantum \(\mathfrak{gl}_{1 | 1}\) and tangle Floer homology ⋮ Diagrammatic state sums for 2D pin-minus TQFTs ⋮ DG structures on odd categorified quantum \(sl(2)\) ⋮ A cubic defining algebra for the Links-Gould polynomial ⋮ Unnamed Item ⋮ Mixed quantum skew Howe duality and link invariants of type \(A\) ⋮ On the decategorification of Ozsváth and Szabó's bordered theory for knot Floer homology ⋮ Polynomial \(6j\)-symbols and states sums ⋮ The Alexander polynomial as quantum invariant of links ⋮ The Links–Gould Invariant as a Classical Generalization of the Alexander Polynomial? ⋮ On the Links–Gould invariant and the square of the Alexander polynomial ⋮ Polynomial link invariants and quantum algebras ⋮ A topological interpretation of Viro's \(\mathfrak{gl}(1|1)\)-Alexander polynomial of a graph ⋮ A quantum categorification of the Alexander polynomial ⋮ Kuperberg invariants for balanced sutured 3-manifolds ⋮ Framed graphs and the non-local ideal in the knot Floer cube of resolutions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Free fermions and the Alexander-Conway polynomial
• Three-manifold invariants derived from the Kauffman bracket
• State sum invariants of 3-manifolds and quantum \(6j\)-symbols
• A state model for the multi-variable Alexander polynomial
• Ribbon graphs and their invariants derived from quantum groups
• Invariants of 3-manifolds via link polynomials and quantum groups
• Reidemeister torsion in knot theory
• MAP COLORING, q-DEFORMED SPIN NETWORKS, AND TURAEV-VIRO INVARIANTS FOR 3-MANIFOLDS
• Colored Vertex Models, Colored IRF Models and Invariants of Trivalent Colored Graphs
• Nonstandard quantum groups and superization
• Quantum invariants of knots and 3-manifolds

This page was built for publication: Quantum relatives of the Alexander polynomial