Alladi Ramakrishnan Hall

An Introduction to Flow Categories

Yash Deshmukh

Columbia University

Flow categories were introduced by Cohen–Jones–Segal as a way to package the data of gradient
trajectories of a Morse function and their breakings. I will introduce flow categories and describe how
the flow category associated with a Morse function can be used to describe higher homotopical data
associated with the underlying manifold in terms of the Morse function. Finally, I will sketch how
these ideas can be adapted to Floer theory. Time permitting, I will report on an ongoing project which
applies these ideas to certain homotopy rigidity questions in symplectic topology.