Derived Lie Infinity-Groupoids and Algebroids in Higher Differential Geometry
Abstract
We study various problems arising in higher geometry using derived Lie $\infty$-groupoids and algebroids. We construct homotopical algebras for derived Lie $\infty$-groupoids and algebroids and study their homotopy-coherent representations. Then we apply these tools in studying singular foliations and their characteristic classes. Finally, we prove an $A_{\infty}$ de Rham theorem and higher Riemann-Hilbert correspondence for foliated manifolds.
Subject Area
Mathematics
Recommended Citation
Zeng, Qingyun, "Derived Lie Infinity-Groupoids and Algebroids in Higher Differential Geometry" (2021). Dissertations available from ProQuest. AAI28775517.
https://repository.upenn.edu/dissertations/AAI28775517