Chennai Mathematical Institute


3.30 pm, Seminar Hall
MSc thesis defence
Discrete Morse theory on moduli spaces of planar polygons

Nachiketa Adhikari
Chennai Mathematical Institute.


Given n real numbers, the space of polygons in the plane having these as side lengths is generically a manifold (M). In this talk, I will introduce a regular CW complex structure on M due to G. Panina. The cells of this structure can be described using partitions of the set {1,...,n}, which give combinatorial insights into how M looks. Discrete Morse theory is a discrete analog of classical Morse theory, used to analyze the topology of a CW complex using special functions called discrete Morse functions. I will discuss a so-called "perfect" Morse function on M. The space M admits a natural involution, and the quotient also has a discrete Morse function which is perfect in some cases. The existence of such a function allows one to construct a CW complex having the minimum number of cells. These and related ideas will be touched upon. Some of the results are new.