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幺半范畴与操作代数研究
幺半范畴与操作代数研究
Yang-Baxter Cohomology with a view toward quantum invariants of knots and knotted surfaces
Yang-Baxter Cohomology with a view toward quantum invariants of knots and knotted surfaces
演讲者
Emanuele Zappala
时间
2026年06月01日 16:00 至 17:00
地点
A3-1-301
线上
Zoom 559 700 6085
(BIMSA)
摘要
Yang–Baxter cohomology provides a natural framework for studying deformations of Yang–Baxter operators and for constructing topological invariants from their perturbative expansions. In this talk, I will describe how infinitesimal deformations and their obstructions are organized by this cohomology theory, and how the resulting perturbative Yang–Baxter operators give rise to quantum invariants of knots and links. With suitable choices of Yang–Baxter operators, this approach recovers quandle cocycle invariants as well as the Jones and Alexander polynomials, placing these constructions within a common deformation-theoretic language.
I will also discuss a Yang–Baxter–Hochschild variant for braided algebras, which unifies aspects of Hochschild and Yang–Baxter cohomology and controls deformations of algebraic structures compatible with Yang–Baxter operators, with examples from Hopf algebras. Finally, I will indicate how analogous ideas extend toward defining perturbative objects that satisfy the Zamolodchikov tetrahedron equation, suggesting a route to quantum invariants of knotted surfaces.
I will also discuss a Yang–Baxter–Hochschild variant for braided algebras, which unifies aspects of Hochschild and Yang–Baxter cohomology and controls deformations of algebraic structures compatible with Yang–Baxter operators, with examples from Hopf algebras. Finally, I will indicate how analogous ideas extend toward defining perturbative objects that satisfy the Zamolodchikov tetrahedron equation, suggesting a route to quantum invariants of knotted surfaces.