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论的分析中发挥着重要作用。拓扑模形式 TMF 理论将这些科学领域与代数拓扑学和代数几何联系起来。弦流形承认 TMF 中的规范方向，就像自旋流形承认实 K 理论中的方向一样。复 K 理论已经为具有 Spin^c 结构（即自旋结构的松弛形式）的流形提供了方向。谱TMF有多种导数，其中一些是复杂可定向的。在该研究项目中，研究了扭曲的字符串结构，人们可以将其称为字符串^c结构。研究了它们中的哪一个为具有各种能级结构的TMF谱或拓扑雅可比形式的谱提供了方向。

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