Morse theory for Lagrangian intersections

Morse Theory on Spaces of Braids and Lagrangian Dynamics

In the first half of the paper we construct a Morse-type theory on certain spaces of braid diagrams. We define a topological invariant of closed positive braids which is correlated with the existence of invariant sets of parabolic flows defined on discretized braid spaces. Parabolic flows, a type of one-dimensional lattice dynamics, evolve singular braid diagrams in such a way as to decrease th...

Lagrangian intersections in contact geometry

Morse Theory

Discrete Morse Theory for Filtrations

Acknowledgements Enumerating all the ways in which I am grateful to Konstantin would essentially double the length of this document, so I'll save all that stuff for my autobiography. But I will note here that he was simultaneously patient, engaged, proactive, and – best of all – ruthlessly determined to refine and sculpt all our vague big-picture ideas into digestible and implementable concrete...

The Morse index theorem for regular Lagrangian systems

In this paper, we prove a Morse index theorem for the index form of regular Lagrangian system with selfadjoint boundary condition.