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Calibrated Submanifolds in \(G_{2}\) Geometry

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Lectures and Surveys on G2-Manifolds and Related Topics

Part of the book series: Fields Institute Communications ((FIC,volume 84))

Abstract

This article summarizes the lecture given by the second author at the Minischool on\(\mathrm {G}_2\) manifolds and related topics” which was held at the Fields Institute in August 2017, and is based on notes made by the first author.

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References

  1. Bott, R., & Tu, L. W. (1982). Differential forms in algebraic topology (Vol. 82), Graduate texts in mathematics. New York: Springer.

    Google Scholar 

  2. Harvey, R., & Lawson, H. B. (1982). Calibrated geometries. Acta Mathematica, 148, 47–157.

    Article  MathSciNet  Google Scholar 

  3. Huybrechts, D. (2005). Complex geometry, Universitext. Berlin: Springer.

    Google Scholar 

  4. Joyce, D. D. (2000). Compact manifolds with special holonomy. Oxford: Oxford University Press.

    Google Scholar 

  5. Karigiannis, S. (2010). Some notes on \(G_{2}\) and Spin(7)  geometry. Recent advances in geometric analysis (Vol. 11, pp. 129–146), Advanced lectures in mathematics. Vienna: International Press. https://arxiv.org/abs/math/0608618.

  6. Karigiannis, S., Lin, C., & Loftin, J. Octonionic-algebraic structure and curvature of the Teichmüller space of \(G_{2}\)manifolds, in preparation.

    Google Scholar 

  7. Kolář, I., Michor, P. W., & Slovák, J. (1993). Natural operations in differential geometry. Berlin: Springer.

    Google Scholar 

  8. Lawson, H. B., & Michelsohn, M. L. (1989). Spin geometry. Princeton: Princeton University Press.

    Google Scholar 

  9. Lee, J.-H., & Leung, N. C. (2008). Instantons and branes in manifolds with vector cross products. Asian Journal of Mathematics, 12, 121–144.

    Article  MathSciNet  Google Scholar 

  10. Leung, N. C., Wang, X., & Zhu, K. (2013). Thin instantons in G2-manifolds and Seiberg-Witten invariants. Journal of Differential Geometry, 95, 419–481.

    Article  MathSciNet  Google Scholar 

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Correspondence to Naichung Conan Leung .

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Chan, K.F., Leung, N.C. (2020). Calibrated Submanifolds in \(G_{2}\) Geometry. In: Karigiannis, S., Leung, N., Lotay, J. (eds) Lectures and Surveys on G2-Manifolds and Related Topics. Fields Institute Communications, vol 84. Springer, New York, NY. https://doi.org/10.1007/978-1-0716-0577-6_4

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