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Chapter 3 gives a short introduction to the spin geometry. After introducing the Clifford algebra and spin groups, spin and spin \({ }^{c}\) structures are formulated, on which the Seiberg–Witten equations will be defined. Next, connections, gauge transformations and Chern–Weil theory are explained, and then Dirac operator is introduced. This chapter is concluded with a short discussion on holomorphic vector bundles.

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Spin Geometry

  • 章节

  • 发表日期：

    2025年

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  • Tsuyoshi Kato,
  • Nobuhiro Nakamura

摘要

Chapter 3 gives a short introduction to the spin geometry. After introducing the Clifford algebra and spin groups, spin and spin \({ }^{c}\) structures are formulated, on which the Seiberg–Witten equations will be defined. Next, connections, gauge transformations and Chern–Weil theory are explained, and then Dirac operator is introduced. This chapter is concluded with a short discussion on holomorphic vector bundles.