Chennai Mathematical Institute

Seminars




MSc (Mathematics) thesis defence talks
2.00 pm, Seminar Hall
Some homology calculations using discrete Morse theory

Naageswaran M.
Chennai Mathematical Institute.
16-04-19


Abstract

A flexible polygon is a piecewise linear closed path in the plane and their moduli space parametrizes them up to isometries. The moduli space of flexible polygons with fixed side lengths is generically a closed manifold which is most of the times non orientable. Inspired by the work G. Panina and her coauthors, in this talk, I will introduce a regular CW complex called the "bi-cyclopermutohedron". This complex is combinatorially defined and is a prototypical example of a virtual polytope. Moreover, for a fixed value of number of sides this complex contains subcomplexes homeomorphic to moduli spaces of flexible polygons. The aim of this talk is to provide an explicit description of the homology groups of bi-cyclopermutohedra. The main tool used for these computations is discrete Morse theory. This talk is based on the joint work with Priyavrat Deshpande and Anurag Singh.