Ashani Dasgupta

ashani.dasgupta@cheenta.com

Category: Topology

  • Linear Connectedness Implies Local Connectedness

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    by

    Ashani Dasgupta
    in ,

    In this note we discuss two notions of connectedness in the context of a metric space. These are Linear Connectedness and Local Connectedness. We wish to prove that linear connectedness implies local connectedness (however the converse is not true). Linear Connectedness or bounded turning is a geometric condition that is defined as follows: Suppose $(X,…

  • Geogebra model for hyperbolic isometries

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    by

    Ashani Dasgupta
    in

    The goals of this GeoGebra model are the following: 1) Input a hyperbolic isometry of the hyperbolic plane using the matrix representation. In other words input a real matrix with determinant 1 and trace more than 2. 2) Programmatically draw the axis. 3) Mark any point P on the hyperbolic plane (upper half plane) 4)…

  • Which manifold is this?

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    by

    Ashani Dasgupta
    in

    This is the first exercise from Thurston’s Three Dimensional Geometry and Topology Vol. 1. Which manifold is this? It is like an old trick. Try following the lines. There are actually 6 loops (circles) in this maze. Here is a color coded picture of it.