Date of Award
2021
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Graduate Group
Mathematics
First Advisor
Jonathan Block
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.
Recommended Citation
Zeng, Qingyun, "Derived Lie Infinity-Groupoids And Algebroids In Higher Differential Geometry" (2021). Publicly Accessible Penn Dissertations. 5120.
https://repository.upenn.edu/edissertations/5120