nonabelian Hodge correspondence

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- Higgs bundle
- stable vector bundle
- Kahler manifold
- flat connection
- Dolbeaut moduli space
- Hodge structure
- P=W conjecture
- Hitchin moduli space

nonabelian Hodge correspondence

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See Higgs bundle

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See lambda connection

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Links to this page

vector bundles

nonabelian Hodge correspondence
unresolved links output

Dolbeaut moduli space in Unsorted/nonabelian Hodge correspondence

Hodge structure in Unsorted/nonabelian Hodge correspondence

Kahler manifold in Unsorted/Calabi-Yau, -Unsorted/four manifold review terms, -Unsorted/nonabelian Hodge correspondence

stable vector bundle in Unsorted/character variety, -Unsorted/nonabelian Hodge correspondence
local system

nonabelian Hodge theory
character variety

\({\mathcal{M}}(\pi_1 \Sigma_g, \operatorname{GL}_n({\mathbf{C}})) = {\mathcal{M}}^{\operatorname{Betti}}_{g, n}\) is a Betti moduli space appearing the in nonabelian Hodge correspondence. Concretely, \begin{align*}{\mathcal{M}}_{g, n}^{\operatorname{Betti}}= \left\{{ \left\{{A_i, B_i}\right\}_{1\leq i \leq g} {~\mathrel{\Big\vert}~}\prod_{1\leq i \leq g}[A_i, B_i] = \operatorname{id}}\right\}/\operatorname{GL}_n({\mathbf{C}}),\end{align*} the moduli stack of representations of \(\pi_1 \Sigma_G\).

- Tags: - #AG #symplectic #todo/too-long - Refs: - https://www.mathi.uni-heidelberg.de/~geodyn/teaching/Theses/MA_2020_Lukas%20D.%20Sauer%20(Albers).pdf#page=3 - Brice Loustau.The complex symplectic geometry of the deformation space of complex projective structures: https://arxiv.org/abs/1406.1821 - Equipped with TQFTs: - https://arxiv.org/pdf/2201.08699.pdf#page=1 - William M. Goldman, The modular group action on real SL(2)-characters of a one-holed torus, Geom. Topol. 7 (2003), 443–486. MR 2026539 - William M Goldman, An exposition of results of fricke, arXiv preprint math/0402103 (2004). - Links: - nonabelian Hodge correspondence - group cohomology - Higgs bundle - Fricke-Vogt theorem - semistable
P=W conjecture

nonabelian Hodge theory
Hodge F-crystal

See harmonic bundle in nonabelian Hodge theory, local system, Higgs bundle, Simpson correspondence.
Higgs bundle

nonabelian Hodge theory

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