Chennai Mathematical Institute


Math MSc/PhD Research Seminar on Nov 7,8,9,11
2.00 pm, Seminar Hall
Moduli spaces of polygons in the Euclidean plane

Nachiketa Adhikari
Chennai Mathematical Institute.


The theory of planar polygon spaces has its origins in the study of mechanical linkages. Given n real numbers, the set of all n-gons in the plane, with these numbers as side lengths, has a natural topological structure. Under certain favourable conditions, this space is a closed, orientable manifold. As a trivial example, there are only two possible triangles of side lengths 3, 4 and 5, if we ignore rotations and translations of the plane. So the resulting configuration space is the 0-sphere.

In this talk, I will introduce some of the key concepts and discuss the main results in the theory. I will also analyze in detail the case n = 4.