Theses Doctoral

A homotopical description of Deligne–Mumford compactifications

Deshmukh, Yash Uday

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.


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More About This Work

Academic Units
Thesis Advisors
Abouzaid, Mohammed
Ph.D., Columbia University
Published Here
May 3, 2023