拓扑学与超弦理论专题
Topics on topology and superstring theory
摘要：
在这篇论文中，我们讨论了有关D-膜的拓扑和超弦背景的一些主题。我们开始与数学审查有关的广义同调和上同调理论和Atiyah-Hirzebruch谱序列，为了提供一个明确的链接，这样的谱序列和Gysin映射。然后，我们回顾了关于线丛和格贝与连接的基本事实。在论文的第二部分，我们应用前面的材料来研究II型超弦背景的几何。本文首先用经典电磁学的方法讨论了D-膜荷的上同调性质，然后从Freed-Witten反常出发，利用Gerbes几何讨论了A-场和B-场的性质，最后讨论了D-膜荷的K-理论分类方法.在最后一部分，我们讨论了一些主题的旋量和pinor，特别注意到不可定向流形。
英文摘要：
In this thesis we discuss some topics about topology and superstring backgrounds with D-branes. We start with a mathematical review about generalized homology and cohomology theories and the Atiyah-Hirzebruch spectral sequence, in order to provide an explicit link between such a spectral sequence and the Gysin map. Then we review the basic facts about line bundles and gerbes with connection. In the second part of the thesis we apply the previous material to study the geometry of type II superstring backgrounds. We first present the cohomological discussion about D-brane charges in analogy with classical electromagnetism, then we use the geometry of gerbes to discuss the nature of the A-field and the B-field as follows from the Freed-Witten anomaly, finally we discuss the K-theoretical approaches to classify D-brane charges. In the last part we discuss some topics about spinors and pinors, with particular attention to non-orientable manifolds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
