BIRS Workshop Lecture Videos

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A retraction of polytopes and integral homology of toric orbifolds. Sarkar, Soumen


In algebraic geometry actions of the torus \( (C^∗)^n \) on algebraic varieties with nice properties produce bridges between geometry and combinatorics. We see a similar bridge called moment map for Hamiltonian action of compact torus on symplectic manifolds. In particular whenever the manifold is compact the image of moment map is a simple polytope, the orbit space of the action. A topological counterpart called quasitoric manifolds were introduced by Davis and Januskiewicz in 1991. They also initiated the topological idea of toric orbifolds. Inspired by this idea, Poddar and Sarkar formalized the definition of (quasi)toric orbifolds. A class of examples of quasitoric orbifolds are weighted progective spaces. In this talk I will discuss the following: 1) Some relations between quasitoric orbifolds and polytopes. 2) Several combinatorial properties of simple polytopes and a combinatorial question. 3) A sufficient condition to compute integral homology of quasitoric orbifolds. This is a joint work with Tony Bahri and Jongbaek Song.

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