Coloured Jones and Alexander polynomials as topological intersections of cycles in configuration spaces

DOI10.1016/j.aim.2024.109993MaRDI QIDQ6651536

Cristina Ana-Maria Anghel

Publication date: 10 December 2024

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

quantum invariantstopological models

Mathematics Subject Classification ID

Knot polynomials (57K14) Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16) Knot theory (57K10)

Cites Work

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• The Lawrence-Krammer-Bigelow representations of the braid groups via \(U_q(\mathfrak{sl}_2)\).
• A functorial approach to the one-variable Jones polynomial
• Homological representations of the Hecke algebra
• A homological representation formula of colored Alexander invariants
• Colored Alexander invariants and cone-manifolds
• A two-variable series for knot complements
• A topological model for the coloured Jones polynomials
• Reading the dual Garside length of braids from homological and quantum representations.
• An integral form of the quantized enveloping algebra of \(sl_2\) and its completions
• A homological model for \(U_q\mathfrak{sl}(2)\) Verma modules and their braid representations
• A topological model for the coloured Alexander invariants
• INVARIANTS OF COLORED LINKS
• HOMOLOGICAL REPRESENTATIONS OF BRAID GROUPS AND KZ CONNECTIONS
• Topological formula of the loop expansion of the colored Jones polynomials

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