Quantization of algebraic invariants through Topological Quantum Field Theories
In 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 condi...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/104007 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/104007 |
| Access Level: | acceso abierto |
| Palabra clave: | TQFT Quantization Monoidal structure Topological Quantum Field Theory Representation variety Topología 1210 Topología |
| Sumario: | In 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. |
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