González Prieto, José Ángel2024-05-142024-05-142023-07González-Prieto, Á. (2023). Quantization of algebraic invariants through Topological Quantum Field Theories. Journal of Geometry and Physics, 189, 104849.0393-044010.1016/j.geomphys.2023.104849https://hdl.handle.net/20.500.14352/1040072023 Acuerdos transformativos CRUEIn this paper we investigate the problem of constructing Topological Quantum Field Theories (TQFTs) to quantize algebraic invariants. We exhibit necessary conditions for quantizability based on Euler characteristics. In the case of surfaces, also provide a partial answer in terms of sufficient conditions by means of almost-TQFTs and almost-Frobenius algebras for wide TQFTs. As an application, we show that the Poincaré polynomial of G-representation varieties is not a quantizable invariant by means of a monoidal TQFTs for any algebraic group G of positive dimension.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articleopen accessTQFTQuantizationMonoidal structureTopological Quantum Field TheoryRepresentation varietyTopología1210 Topología