Twisted String-structures

• Applicant: Professor Dr. Gerd Laures
• Subject Area: Mathematics
• Term: from 2016 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 322563960

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.

• DFG Programme: Research Grants