Quaternionic geometry and elliptic genus

四元几何和椭圆亏格

• 批准号: 0405281
• 负责人: Haydee Herrera
• 金额: --
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-15 至 2007-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0405281&HistoricalAwards=false
• 关键词: Quaternionic; geometry; elliptic; genus

AbstractAward: DMS-0405281Principal Investigator: Haydee HerreraThis research proposal focuses on the study of the topology ofmanifolds with finite second homotopy group and the DifferentialGeometry of quaternionic- Kaehler manifolds. The emphasis of theproject is on the determination of analytical and topologicalinvariants of the manifolds, such as the signature, A-roof-genusand elliptic genera. Following the evidence from our previousresearch, we propose to apply the aforementioned theory toconcrete Geometric Analysis/Differential Geometryproblems. Furthermore, this study has applications to AlgebraicGeometry (via twistor transform) and to Theoretical Physics,since the manifolds under consideration are of interest in sigmamodels and in String Theory.My research interests are concerned with the study of certainspaces of large dimension, called quaternion-Kaehlermanifolds. In the quest for understanding the universe,physicists have developed many and very sophisticated models,such as Relativity Theory and more recently String Theory, thathelp explain and predict phenomena observed in the Universe. Oneof the leading physicists of our times, E. Witten, discoveredthat quaternion-Kaehler manifolds appear in the formulation ofcertain Quantum Field Theories. My research focuses on findingthe possible shapes and properties of quaternion- Kaehlermanifolds.

摘要奖项：DMS-0405281 首席研究员：Haydee Herrera 本研究计划重点研究具有有限第二同伦群的流形拓扑和四元-凯勒流形的微分几何。该项目的重点是确定流形的分析和拓扑不变量，例如签名、A-屋顶亏格和椭圆亏格。根据我们之前研究的证据，我们建议将上述理论应用于具体的几何分析/微分几何问题。此外，这项研究还应用于代数几何（通过扭量变换）和理论物理，因为所考虑的流形在西格玛模型和弦理论中很有趣。我的研究兴趣涉及某些大维空间的研究，称为四元数-凯勒流形。在寻求理解宇宙的过程中，物理学家开发了许多非常复杂的模型，例如相对论和最近的弦理论，有助于解释和预测在宇宙中观察到的现象。 我们这个时代的一位顶尖物理学家 E. Witten 发现四元数-凯勒流形出现在某些量子场论的公式中。 我的研究重点是寻找四元数凯勒流形的可能形状和性质。