Hodge theory of representation varieties via Topological Quantum Field Theories
González-Prieto, Ángel
arXiv, 1810.09714 / Harvested from arXiv
Text on arXiv
In this paper, we show how lax monoidal TQFTs can be used as an effective computational method of the $K$-theory image of the Hodge structure of representation varieties. In particular, we perform the calculation for parabolic $\mathrm{SL}_2(\mathbb{C})$-representation varieties over a closed orientable surface of arbitrary genus and any number of marked points with holonomies of Jordan type. This technique is based on a building method of lax monoidal TQFTs of physical inspiration that generalizes the construction of Gonz\'alez-Prieto, Logares and Mu\~noz.
Publié le : 2018-10-23
Classification:  Mathematics - Algebraic Geometry,  Mathematical Physics,  Mathematics - Category Theory,  Mathematics - Representation Theory,  14C30 (Primary) 57R56, 14D07, 14D21 (Secondary) 
@article{1810.09714,
     author = {Gonz\'alez-Prieto, \'Angel},
     title = {Hodge theory of representation varieties via Topological Quantum Field
  Theories},
     journal = {arXiv},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1810.09714}
}

González-Prieto, Ángel. Hodge theory of representation varieties via Topological Quantum Field
  Theories. arXiv, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/1810.09714/