2023 Theses Doctoral
A homotopical description of Deligne–Mumford compactifications
In this thesis I will give a description of the Deligne–Mumford properad expressing it as the result of homotopically trivializing S¹ families of annuli (with appropriate compatibility conditions) in the properad of smooth Riemann surfaces with parameterized boundaries. This gives an analog of the results of Drummond-Cole and Oancea–Vaintrob in the setting of properads. We also discuss a variation of this trivialization which gives rise to a new partial compactification of Riemann surfaces relevant to the study of operations on symplectic cohomology.
Files
- Deshmukh_columbia_0054D_17801.pdf application/pdf 1.05 MB Download File
More About This Work
- Academic Units
- Mathematics
- Thesis Advisors
- Abouzaid, Mohammed
- Degree
- Ph.D., Columbia University
- Published Here
- May 3, 2023