- On the compactification of bounded edge flow trees
- Project Year:
2021
- REU Student (s):
Kenneth Blakey | Brown University RI
- Student 1 Institution:
Brown University
- Project Mentor:
Christopher Woodward
- Project Mentor Area:
Mathematics
- Project Abstract:
Let L⊂J^1(M) be a closed Legendrian submanifold of the 1-jet space of a closed Riemannian manifold. We conjecture that the moduli space of flow trees with at most n edges has a natural compactification given by the moduli space of broken flow trees with at most n edges. In order to solve this one would have to compactify the various moduli spaces of gradient trajectories of local function differences determined by L. We establish a compactification of the moduli space of Morse trajectories - gradient trajectories connecting critical points of a fixed local function difference - similar to the compactification in standard Morse theory.
