Research Seminar 1
Date/Time: 15.09.2021, 10:00 am.
Building planar polygon spaces from the projective Coxetercomplex
Navnath Daundkar
Chennai Mathematical Institute.
15-09-21

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Abstract

The moduli space of planar polygons with generic side lengths is a smooth, closed manifold. It is known that these spaces contain the real moduli space of genus zero curves as a dense subset. Hence form the compactifications of the real moduli space of genus zero curves. Kapranov showed that the real points of Deligne-Mumford-Knudson compactification can be obtained from the projective Coxeter complex of type A by blowing up along the minimal building set. In this talk I will show that the planar polygon spaces can also be obtained from the projective Coxeter complex of type A by performing an iterative cellular surgery along the subcollection of the minimal building set. Interestingly this subcollection is generated by the combinatorial data associated with the length vector called the genetic code. If time permits I will also show how to realize some planar polygon spaces as the real Bott manifolds and consequently compute their rational Betti numbers.