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.
07-11-16

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Abstract

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.