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.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/wbaz-s752 |
| Date | January 2023 |
| Creators | Deshmukh, Yash Uday |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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