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Lectures on Special Lagrangian Submanifolds

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arxiv math/9907034 v1 pith:ZLDSZCOU submitted 1999-07-06 math.DG hep-thmath.AG

Nigel Hitchin This is my paper · ORCID
classification math.DGhep-thmath.AG
keywords lagrangianspecialsubmanifoldsallowsapproachappropriatecalabi-yaucase
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These notes consist of a study of special Lagrangian submanifolds of Calabi-Yau manifolds and their moduli spaces. The particular case of three dimensions, important in string theory, allows us to introduce the notion of gerbes. These offer an appropriate language for describing many significant features of the Strominger-Yau-Zaslow approach to mirror symmetry.

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Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Differential Models for the Anderson Dual to Twisted $\mathrm{Spin}^c$-Bordism and a Twisted Anomaly Map

    math.AT 2025-10 conditional novelty 8.0 of 10

    Differential models for twisted Spin^c-bordism and its Anderson dual are constructed, together with a twisted anomaly map from differential twisted K-theory.

  2. Topological Twisting of 4d $\mathcal{N}=2$ Supersymmetric Field Theories

    hep-th 2024-11 conditional novelty 8.0 of 10

    For any 4d N=2 theory, topologically twisted partition functions depend on the diffeomorphism type, 't Hooft fluxes, and a generalized spin-c structure.

  3. On Quantum Aspects of 1-Form Symmetries I: BV-BRST Cohomology and Anomaly Polynomials

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    Develops Čech-de Rham bicomplex from gerbe data for BV-BRST cohomology of U(1) 2-form gauge theories and anomaly polynomials of 1-form symmetries.

  4. 3-Crossed Module Structure in the Five-Dimensional Topological Axion Electrodynamics

    hep-th 2026-02 unverdicted novelty 6.0 of 10

    The five-dimensional topological axion electrodynamics is shown to possess a 3-crossed module structure through modified Stueckelberg couplings required for background gauge invariance.

  5. Non-archimedean topological mirror symmetry for $SL_n$ and $PGL_n$ Higgs bundles

    math.AG 2025-07 accept novelty 6.0 of 10

    The author proves an equality of gerbe-twisted p-adic integrals on SLn and PGLn Higgs bundle moduli spaces for arbitrary rank and degree, generalizing the coprime-case result of Groechenig, Wyss, and Ziegler.

  6. Parametrized topological phases in 1d and T-duality

    math-ph 2024-12 conditional novelty 4.0 of 10

    Families of 1d topological phases are classified by H^3(M,Z) via Hilbert-Schmidt bundles, and topological T-duality relates families on circle-bundle parameter spaces with different higher Berry classes.

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