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Introduction to Symplectic Geometry and Fukaya Category

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Superschool on Derived Categories and D-branes (SDCD 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 240))

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Abstract

We give a brief introduction to symplectic manifolds and Fukaya Category in this manuscript.

This lecture note is written for a talk in Superschool on derived categories and D-branes in July, 2016 at University of Alberta.

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References

  1. Dusa McDuff, Dietmar Salamon, Introduction to Symplectic Topology, Oxford Science Publications, 2nd edition.

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  2. Peter Albers, A Lagrangian Piunikhin-Salamon-Schwarz morphism and two comparison homomorphisms in Floer homology, arXiv:math/0512037

  3. Leonid Polterovich, Monotome Lagrange submanifolds of linear spaces and the Maslov class in cotangent bundles. Mathematische Zeitschrift, vol 207, 1991, No.2, 217–222.

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  4. Denis Auroux, A beginner’s introduction to Fukaya categories, arXiv:1301.7056

  5. Paul Seidel, Fakaya categories and Picard-Lefschetz Theory. European Mathematical Society, 2008.

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Acknowledgements

I am grateful to David Favero, Matthew Ballard and Eric Sharpe for organizing this super school and giving me the chance to present this material. I am also grateful to my advisor Mohammed Abouzaid for giving me so much guidance along the way.

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Authors and Affiliations

  1. Columbia College of Columbia University in New York City, New York, NY, USA

    Alex Zhongyi Zhang

Authors
  1. Alex Zhongyi Zhang
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Correspondence to Alex Zhongyi Zhang .

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Editors and Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, South Carolina, USA

    Matthew Ballard

  2. Department of Mathematics and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada

    Charles Doran

  3. Department of Mathematics and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada

    David Favero

  4. Department of Physics, Virginia Tech, Blacksburg, Virginia, USA

    Eric Sharpe

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Zhang, A.Z. (2018). Introduction to Symplectic Geometry and Fukaya Category. In: Ballard, M., Doran, C., Favero, D., Sharpe, E. (eds) Superschool on Derived Categories and D-branes. SDCD 2016. Springer Proceedings in Mathematics & Statistics, vol 240. Springer, Cham. https://doi.org/10.1007/978-3-319-91626-2_11

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