Asphericity of chain spaces

Abstract: The moduli space of chains (i.e. piece-wise linear paths) in the plane with generic side lengths is a smooth, closed manifold. It turns out that this manifold has a natural action of discrete torus such that the quotient under this action is a simple polytope, making it into a small cover (in fact a real toric variety). In this talk I will show that in every dimension there are three length vectors for which the moduli space is aspherical. If time permits I will also show that the quotient polytope depends only on the combinatorial data, called the genetic code of the length vector. This is ongoing work with my adviser Priyavrat Deshpande.

commutative algebraalgebraic topologycombinatorics

Audience: researchers in the topic

Applications of Combinatorics in Algebra, Topology and Graph Theory

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