- Morse Flow Trees and Chain Complexes
- Project Year:
2021
- REU Student (s):
Sangjun Ko | Rutgers University-New Brunswick NJ
- Student 1 Institution:
Rutgers University-New Brunswick
- Project Mentor:
Christopher Woodward
- Project Mentor Area:
Mathematics
- Project Abstract:
Morse flow trees are a tool to compute Legendrian contact homology, and Ekholm has showed that these flow trees have a correspondence with certain types of rigid pseudoholomorphic disks in T*M if M is a manifold. There are still some open questions regarding the space of these flow trees, some of which we investigated this summer. Our aim here will be to describe some of the background material required to understand the definition of Morse flow trees. First we discuss the elements of Morse Theory and define the Morse complex; then we discuss a little bit of symplectic topology so that we define what a Lagrangian submanifold is; finally, we give the definition of a flow tree and introduce a problem related to it.
