Twisted String-structures

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

• Final Report Year: 2020

Final Report Abstract

The spectrum of topological modular forms T mf and its derivatives T mf1 (N ) with level structures connects the machinery of Algebraic Topology and to Algebraic Geometry to the analysis on loop spaces and to quantum field theories. String manifolds admit a canonical orientation in T mf in the same way as spin manifolds admit an orientation in real K-theory. The theories T mf1 (N ) are known to be complex orientable but it is unsolved which orientations are highly structured with respect to commutativity. The research project solved the problem to find all such E∞-orientations with respect to SU-bordism.

Publications

• Cannibalistic classes of string bundles, Manuscripta Math., 156 (2018), no. 3-4, 273–298
  Gerd Laures and Martin Olbermann
  (See online at https://doi.org/10.1007/s00229-017-0978-8)
• Towards a splitting of the K(2)-local string bordism spectrum, Proc. Amer. Math. Soc., 147 (2019), no. 1, 399–410
  Gerd Laures and Björn Schuster
  (See online at https://doi.org/10.1090/proc/14190)