Twisted String-structures

扭弦结构

• 批准号: 322563960
• 负责人: Professor Dr. Gerd Laures
• 金额: --
• 依托单位: Lehrstuhl Topologie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/322563960?language=en
• 关键词: Twisted; String; structures

String structures play an important role in the analysis on loop spaces and in quantum field theories. The theory of topological modular forms TMF connects these areas of science to the machinery of Algebraic Topology and to Algebraic Geometry. String manifolds admit a canonical orientation in TMF in the same way as spin manifolds admit an orientation in real K-theory. Complex K-theory already provides orientations for manifolds with a Spin^c-structure, that is, a relaxed form of a Spin-structure. The spectrum TMF has various derivatives, some of which are complex orientable. In the research project, twisted String-structures are studied which one might call String^c-structures. It is investigated which of them provide orientations for the spectrum of TMF with various level structures or for the spectrum of topological Jacobi forms.

弦结构在循环空间和量子场理论的分析中起着重要作用。拓扑模块化形式的理论TMF将这些科学领域连接到代数拓扑的机械和代数几何形状。字符串歧管以与Spin歧管相同的方式接受TMF中的规范取向。复杂的K理论已经提供了具有自旋^C结构的歧管的方向，即自旋结构的轻松形式。频谱TMF具有各种衍生物，其中一些衍生物可取向。在研究项目中，研究了扭曲的弦线结构，其中可能称为字符串结构。研究了哪些为TMF频谱提供了各种级别的结构或拓扑雅各比形式的频谱的方向。

项目成果

Towards a splitting of the $K(2)$-local string bordism spectrum

走向$K(2)$-局部弦波谱的分裂

• DOI: 10.1090/proc/14190
• 发表时间: 2019
• 期刊: Proceedings of the American Mathematical Society
• 影响因子: 1
• 作者: Gerd Laures;Björn Schuster
• 通讯作者: Björn Schuster

Cannibalistic classes of string bundles

同类相食的弦束

• DOI: 10.1007/s00229-017-0978-8
• 发表时间: 2018
• 期刊: manuscripta mathematica
• 影响因子: 0.6
• 作者: Gerd Laures;Martin Olbermann
• 通讯作者: Martin Olbermann